Journal articles: 'Rotation averaging'

1

Hartley, Richard, Jochen Trumpf, Yuchao Dai, and Hongdong Li. "Rotation Averaging." International Journal of Computer Vision 103, no. 3 (January 30, 2013): 267–305. http://dx.doi.org/10.1007/s11263-012-0601-0.

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Gao, Xiang, Lingjie Zhu, Zexiao Xie, Hongmin Liu, and Shuhan Shen. "Incremental Rotation Averaging." International Journal of Computer Vision 129, no. 4 (January 16, 2021): 1202–16. http://dx.doi.org/10.1007/s11263-020-01427-7.

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Chatterjee, Avishek, and Venu Madhav Govindu. "Robust Relative Rotation Averaging." IEEE Transactions on Pattern Analysis and Machine Intelligence 40, no. 4 (April 1, 2018): 958–72. http://dx.doi.org/10.1109/tpami.2017.2693984.

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Gao, Xiang, Jiazheng Luo, Kunqian Li, and Zexiao Xie. "Hierarchical RANSAC-Based Rotation Averaging." IEEE Signal Processing Letters 27 (2020): 1874–78. http://dx.doi.org/10.1109/lsp.2020.3031759.

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Reich, M., and C. Heipke. "GLOBAL ROTATION ESTIMATION USING WEIGHTED ITERATIVE LIE ALGEBRAIC AVERAGING." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences II-3/W5 (August 20, 2015): 443–49. http://dx.doi.org/10.5194/isprsannals-ii-3-w5-443-2015.

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In this paper we present an approach for a weighted rotation averaging to estimate absolute rotations from relative rotations between two images for a set of multiple overlapping images. The solution does not depend on initial values for the unknown parameters and is robust against outliers. Our approach is one part of a solution for a global image orientation. Often relative rotations are not free from outliers, thus we use the redundancy in available pairwise relative rotations and present a novel graph-based algorithm to detect and eliminate inconsistent rotations. The remaining relative rotations are input to a weighted least squares adjustment performed in the Lie algebra of the rotation manifold SO(3) to obtain absolute orientation parameters for each image. Weights are determined using the prior information we derived from the estimation of the relative rotations. Because we use the Lie algebra of SO(3) for averaging no subsequent adaptation of the results has to be performed but the lossless projection to the manifold. We evaluate our approach on synthetic and real data. Our approach often is able to detect and eliminate all outliers from the relative rotations even if very high outlier rates are present. We show that we improve the quality of the estimated absolute rotations by introducing individual weights for the relative rotations based on various indicators. In comparison with the state-of-the-art in recent publications to global image orientation we achieve best results in the examined datasets.

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Dong, Yihong, Lunchen Xie, and Qingjiang Shi. "Efficient Algorithms for Rotation Averaging Problems." Proceedings of the ACM on Computer Graphics and Interactive Techniques 4, no. 1 (April 26, 2021): 1–16. http://dx.doi.org/10.1145/3451263.

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The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of a fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.

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Liu, Yue, Tian Tian Ren, and Jin Shan Guo. "The Absolute Measurement Deviation of Rotational Averaging Mirror Surface Based on the Finite Element Method." Advanced Materials Research 998-999 (July 2014): 481–85. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.481.

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In order to obtain higher levels of surface form accuracy, it adopted rotational averaging method, analyzed the supporting position and rotation-angle deviation of the model via the finite element analysis technology. You can see that the mirror surface Peak Valley Value and Root Mean Square Value, increase with the increase of supporting and angle deviation. Thus, to realize high precision mirror surface detection, it should guarantee the supporting position and rotation-angle deviation of the model at the same time. The measurement precision of rotational averaging method absolute measurement can achieve one percent wavelength (λ=632.8nm),it is far superior to the other detection technology in absolute measurement.

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Brynte, Lucas, Viktor Larsson, José Pedro Iglesias, Carl Olsson, and Fredrik Kahl. "On the Tightness of Semidefinite Relaxations for Rotation Estimation." Journal of Mathematical Imaging and Vision 64, no. 1 (October 7, 2021): 57–67. http://dx.doi.org/10.1007/s10851-021-01054-y.

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AbstractWhy is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand–eye calibration, and rotation averaging. We characterize the extreme points and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.

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Tweed, D., D. Sievering, H. Misslisch, M. Fetter, D. Zee, and E. Koenig. "Rotational kinematics of the human vestibuloocular reflex. I. Gain matrices." Journal of Neurophysiology 72, no. 5 (November 1, 1994): 2467–79. http://dx.doi.org/10.1152/jn.1994.72.5.2467.

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1. This series of three papers aims to describe the three-dimensional, kinematic input-output relations of the rotational vestibuloocular reflex (VOR) in humans, and to identify the functional advantages of these relations. In this first paper the response to sinusoidal rotation in darkness at 0.3 Hz, maximum speed 37.5%/s, was quantified by the use of the three-dimensional analogue of VOR gain: a 3 x 3 matrix where each element describes the dependence of one component (torsional, vertical, or horizontal) of eye velocity on one component of head velocity. 2. The three matrix elements indicating collinear gains (i.e., dependence of torsional eye velocity on torsional head velocity, vertical on vertical, and horizontal on horizontal) were smaller than the -1's required for optimal retinal image stabilization. Of these three the torsional gain was weakest: -0.37 for rotation about an earth-vertical axis, versus -0.73 and -0.64 for vertical and horizontal gains. Matrix elements indicating cross talk were mostly negligible. There was a tendency to leftward eye rotation in response to clockwise head motion, but this was not statistically significant. 3. VOR responses were compared for rotation about earth-vertical and earth-horizontal axes. The varying otolith input due to the rotation of the gravity vector relative to the head during earth-horizontal axis rotation made no difference to the collinear gains. 4. There were no consistent phase leads or lags except for a torsional phase lead of up to 10 degrees, usually more marked for clock-wise head rotation versus counterclockwise, and for oblique axis rotations versus purely torsional. 5. Torsional gain was magnified, averaging -0.52, when the torsional component of head rotation was only a small part of a predominantly vertical or horizontal rotation, i.e., when the axis of head rotation was near the frontal plane. Because most natural head rotations occur about such axes, the torsional VOR is probably somewhat stronger than the response to pure torsion would suggest. 6. The speed of eye rotation in response to a given stimulus varied widely among subjects, but the direction of rotation was much more uniform. For head rotations about oblique axes out of the frontal plane, there was a systematic misalignment of eye and head axes, with eye axes tilted toward the frontal plane. These findings can be explained on the basis of a strategy where the VOR balances the muscular effort of rotating the eyes against the cost of retinal slip.

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Reich, Martin, Michael Ying Yang, and Christian Heipke. "Global robust image rotation from combined weighted averaging." ISPRS Journal of Photogrammetry and Remote Sensing 127 (May 2017): 89–101. http://dx.doi.org/10.1016/j.isprsjprs.2017.01.011.

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Painter, K. M., D. L. Young, D. M. Granatstein, and D. J. Mulla. "Combining alternative and conventional systems for environmental gains." American Journal of Alternative Agriculture 10, no. 2 (June 1995): 88–96. http://dx.doi.org/10.1017/s0889189300006214.

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AbstractTwo conventional cropping systems (winter wheat/dry peas and winter wheat/spring barley/dry peas) in the dryland grain region of southeastern Washington were compared with several alternative systems regarding profitability and environmental impacts. Two of the alternative systems use green manure crops and have low fertilizer and pesticide requirements. The remaining two are otherwise conventional rotations modified to include soil-building crops, bluegrass seed and rapeseed.Estimates of annual off-site erosion damage ranged from $6.56 to $20.50 per rotational acre, while on-site damage estimates ranged from $0.50 to $1.55 per rotational acre. Estimated leaching losses of pesticides to a water table 3.6 feet deep were negligible, but significant leaching losses of nitrate-N were predicted to occur from fall-applied inorganic fertilizer.Including bluegrass in a conventional grain rotation increased estimated net returns over variable costs by 16% and decreased soil loss by 33% compared with the most profitable conventional rotation. The next most profitable alternative system, rapeseed plus a conventional grain rotation, had slightly higher net returns over variable costs than the second most profitable conventional rotation, with slightly less soil loss. When fixed costs of machinery depreciation and land are included, the alternative systems fared relatively better. An experimental wheat/pea/medic system had higher projected net returns over total costs than the most profitable conventional rotation, while averaging just one-third as much soil loss per year. A wheat/barley/sweetclover green manure rotation was similar in profitability to the less profitable conventional rotation, but had only two-thirds as much soil loss.We constructed a mixed-integer linear programming model to determine the profitmaximizing combination of conventional and alternative rotations under 1990 farm bill provisions. Planting all or nearly all land to the bluegrass plus conventional grain rotation maximized returns over total costs for high, medium, and low program crop price scenarios. Farmers maximized profit by participating in both the wheat and barley programs under the low price scenario, only in the wheat program with moderate prices, and in neither the wheat nor the barley program under the high price scenario.

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Wang, X., F. Rottensteiner, and C. Heipke. "ROBUST IMAGE ORIENTATION BASED ON RELATIVE ROTATIONS AND TIE POINTS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2 (May 28, 2018): 295–302. http://dx.doi.org/10.5194/isprs-annals-iv-2-295-2018.

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In this paper we present a novel approach for image orientation by combining relative rotations and tie points. First, we choose an initial image pair with enough correspondences and large triangulation angle, and we then iteratively add clusters of new images. The rotation of these newly added images is estimated from relative rotations by single rotation averaging. In the next step, a linear equation system is set up for each new image to solve the translation parameters with triangulated tie points which can be viewed in that new image, followed by a resection for refinement. Finally, we optimize the cluster of reconstructed images by local bundle adjustment. We show results of our approach on different benchmark datasets. Furthermore, we orient several larger datasets incl. unordered image datasets to demonstrate the robustness and performance of our approach.

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Zha, Jun, Yaolong Chen, and Penghai Zhang. "Relationship between elliptical form error and rotation accuracy of hydrostatic journal bearing." Industrial Lubrication and Tribology 69, no. 6 (November 13, 2017): 905–11. http://dx.doi.org/10.1108/ilt-08-2016-0192.

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Purpose The form error of shaft and hole parts is inevitable because of the machining error caused by rotation error of tool axis in machine tools where the elliptical form error is the most common in shaft and bearing bush. The purpose of this paper is to present the relationship between the elliptical form error and rotation accuracy for hydrostatic journal bearing in precision spindle and rotation table. Design/methodology/approach An error averaging effect model of hydrostatic journal bearing is established by using Reynolds equation, pressure boundary conditions, flux continuity equation of the land and kinetic equation of shaft in hydrostatic journal bearing. The effects of shaft and bearing bush on rotation accuracy were analyzed quantitatively. Findings The results reveal that the effect of shaft elliptical form error on rotation accuracy was six times larger than bearing bush. Therefore, to improve the rotation accuracy of hydrostatic journal bearing in spindle or rotation table, the machining error of shaft should be controlled carefully. Originality/value An error averaging model is proposed to evaluate the effect of an elliptical form error on rotation accuracy of hydrostatic journal bearings, which solves the Reynolds equation, the flux continuity equation and the kinetic equation. The determination of form error parameters of shaft and bearing bush can be yielded from finding results of this study for precision design of hydrostatic journal bearings.

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Tornow, F., H. W. Barker, Velázquez Blázquez, C. Domenech, and J. Fischer. "EarthCARE’s Broadband Radiometer: Uncertainties Associated with Cloudy Atmospheres." Journal of Atmospheric and Oceanic Technology 35, no. 11 (November 2018): 2201–11. http://dx.doi.org/10.1175/jtech-d-18-0083.1.

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AbstractThe Earth Clouds, Aerosol and Radiation Explorer (EarthCARE) satellite’s Broadband Radiometer (BBR) consists of three telescopes and a rotating chopper drum (CD). Together they yield alternating measurements of total wave (TW; 0.25 to >50 μm) and shortwave (SW; 0.25–4 μm) radiances with point spread functions that translate to 0.6-km-diameter pixels. The mission requires that SW and TW radiances be averaged over 100-km2 domains. Correspondingly, the average longwave (LW) radiances are the differences between TW and SW averages. It is shown that impacts on domain-average nadir radiances resulting from alternating samples of TW and SW signals for realistic cloudy atmospheres are sensitive to the variance of cloudy-sky radiances, CD rotation rate, and along-track length of averaging domains. Over domains measuring 5 × 21 km2 and at a 50% rotation rate, uncertainties reached up to 3.2 and 4.1 W m−2 sr−1 for SW and TW radiances, respectively. The BBR’s design allows for in-flight alteration of the CD rate. An approximate method is provided for estimating SW and LW uncertainties resulting from the CD rate. While the nominal rotation rate meets EarthCARE’s mission requirements, reducing below 75% of that rate will lead to uncertainties for domain-average LW radiances that will often exceed mission requirements. This could be mitigated by increasing the size of averaging domains but that would compromise the BBR’s role in EarthCARE’s radiative closure assessment program. Uncertainties for off-nadir radiances are largely free of impacts arising from changes to the CD rotation rate.

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Wang, X., T. Xiao, and Y. Kasten. "A HYBRID GLOBAL IMAGE ORIENTATION METHOD FOR SIMULTANEOUSLY ESTIMATING GLOBAL ROTATIONS AND GLOBAL TRANSLATIONS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2020 (August 3, 2020): 95–104. http://dx.doi.org/10.5194/isprs-annals-v-2-2020-95-2020.

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Abstract. In recent years, the determination of global image orientation, i.e. global SfM, has gained a lot of attentions from researchers, mainly due to its time efficiency. Most of the global methods take relative rotations and translations as input for a two-step strategy comprised of global rotation averaging and global translation averaging. This paper by contrast presents a hybrid approach that aims to solve global rotations and translations simultaneously, but hierarchically. We first extract an optimal minimum cover connected image triplet set (OMCTS) which includes all available images with a minimum number of triplets, all of them with the three related relative orientations being compatible to each other. For non-collinear triplets in the OMCTS, we introduce some basic characterizations of the corresponding essential matrices and solve for the image pose parameters by averaging the constrained essential matrices. For the collinear triplets, on the other hand, the image pose parameters are estimated by relative orientation using the depth of object points from individual local spatial intersection. Finally, all image orientations are estimated in a common coordinate frame by traversing every solved triplet using a similarity transformation. We show results of our method on different benchmarks and demonstrate the performance and capability of the proposed approach by comparing with other global SfM methods.

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Cass, Joseph R., and Harry Settles. "Ankle Instability: In Vitro Kinematics in Response to Axial Load." Foot & Ankle International 15, no. 3 (March 1994): 134–40. http://dx.doi.org/10.1177/107110079401500308.

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This study was undertaken to elucidate the kinematics of hindfoot instability. An axial load was applied to the inverted hindfoot. Unlike prior studies, axial rotation was not constrained. Using computerized tomography, measurements were made on the axial views of external or internal rotation of the leg, talus, and calcaneus. On the coronal views, tilting of the talus at the ankle and subtalar joints was assessed. No tilting of the talus in the mortise occurred with isolated release of the anterior talofibular (ATF) or calcaneofibular (CF) ligament. In every specimen, talar tilt occurred only after both ligaments were released, averaging 20.6°. External rotation of the leg occurred with inversion averaging 11.1° in the intact specimen. The leg averaged a further external rotation of 4.9° after ATF release and 12.8° further than the intact inverted specimens when both ligaments (ATF-CF) had been released. In earlier reports on the subject, the articular surfaces were believed to be the main constraint against tilting of the talus. In those studies, either axial rotation was constrained while inversion was allowed, or vice versa. Based on the data reported here, the ATF and the CF work in tandem to prevent tilting of the talus, and the articular surfaces do not seem to prevent tilting of the talus in the mortise.

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Reich, M., and C. Heipke. "A global approach for image orientation using Lie algebraic rotation averaging and convex L_∞ minimisation." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3 (August 11, 2014): 265–72. http://dx.doi.org/10.5194/isprsarchives-xl-3-265-2014.

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In this paper we present a new global image orientation approach for a set of multiple overlapping images with given homologous point tuples which is based on a two-step procedure. The approach is independent on initial values, robust with respect to outliers and yields the global minimum solution under relatively mild constraints. The first step of the approach consists of the estimation of global rotation parameters by averaging relative rotation estimates for image pairs (these are determined from the homologous points via the essential matrix in a pre-processing step). For the averaging we make use of algebraic group theory in which rotations, as part of the special orthogonal group SO(3), form a Lie group with a Riemannian manifold structure. This allows for a mapping to the local Euclidean tangent space of SO(3), the Lie algebra. In this space the redundancy of relative orientations is used to compute an average of the absolute rotation for each image and furthermore to detect and eliminate outliers. In the second step translation parameters and the object coordinates of the homologous points are estimated within a convex L∞ optimisation, in which the rotation parameters are kept fixed. As an optional third step the results can be used as initial values for a final bundle adjustment that does not suffer from bad initialisation and quickly converges to a globally optimal solution. We investigate our approach for global image orientation based on synthetic data. The results are compared to a robust least squares bundle adjustment. In this way we show that our approach is independent of initial values and more robust against outliers than a conventional bundle adjustment.

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Pechenev, A. V. "The averaging of systems with a hierarchy of phase rotation speeds." Journal of Applied Mathematics and Mechanics 56, no. 1 (January 1992): 20–24. http://dx.doi.org/10.1016/0021-8928(92)90091-l.

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Dannenberg, Rand. "Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity." Symmetry 12, no. 3 (March 4, 2020): 398. http://dx.doi.org/10.3390/sym12030398.

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Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

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Tashman, Scott, and William Anderst. "In-Vivo Measurement of Dynamic Joint Motion Using High Speed Biplane Radiography and CT: Application to Canine ACL Deficiency." Journal of Biomechanical Engineering 125, no. 2 (April 1, 2003): 238–45. http://dx.doi.org/10.1115/1.1559896.

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Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (−0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31° for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71° for flexion/extension, 0.90° for internal/external rotation, and 0.40° for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.

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Zeitlin, V. "Remarks on rotating shallow-water magnetohydrodynamics." Nonlinear Processes in Geophysics 20, no. 5 (October 29, 2013): 893–98. http://dx.doi.org/10.5194/npg-20-893-2013.

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Abstract. We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion of the baroclinic effects. A quasi-geostrophic version of the model, both in barotropic and in baroclinic cases, is derived in the limit of strong rotation. The basic properties of the model(s) are sketched, including the stabilizing role of magnetic fields in the baroclinic version.

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PLAUT, E., and F. H. BUSSE. "Low-Prandtl-number convection in a rotating cylindrical annulus." Journal of Fluid Mechanics 464 (August 10, 2002): 345–63. http://dx.doi.org/10.1017/s0022112002008923.

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Motivated by recent experimental results obtained in a low-Prandtl-number fluid (Jaletzky 1999), we study theoretically the rotating cylindrical annulus model with rigid boundary conditions. A boundary layer theory is presented which allows a systematic study of the linear properties of the system in the asymptotic regime of very fast rotation rates. It shows that the Stewartson layers have a (de)stabilizing influence at (high) low Prandtl numbers. In the weakly nonlinear regime and for low Prandtl numbers, a strong retrograde mean flow develops at quadratic order. The Poiseuille part of this mean flow is determined by an equation obtained by averaging of the Navier–Stokes equation. It thus gives rise to a new global-coupling term in the envelope equation describing modulated waves, which can be used for other systems. The influence of this global-coupling term on the sideband instabilities of the waves is studied. In the strongly nonlinear regime, the waves restabilize against these instabilities at small rotation rates, but they are destabilized by a short-wavelength mode at larger rotation rates. We also find an inversion in the dependence of the amplitude on the Rayleigh number at low Prandtl numbers and intermediate rotation rates.

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Shatina, A. V., M. I. Djioeva, and L. S. Osipova. "Mathematical Model of Satellite Rotation near Spin-Orbit Resonance 3:2." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd220803.

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This paper considers the rotational motion of a satellite equipped with flexible viscoelastic rods in an elliptic orbit. The satellite is modeled as a symmetric rigid body with a pair of flexible viscoelastic rods rigidly attached to it along the axis of symmetry. A planar case is studied, i. e., it is assumed that the satellite’s center of mass moves in a Keplerian elliptic orbit lying in a stationary plane and the satellite’s axis of rotation is orthogonal to this plane. When the rods are not deformed, the satellite’s principal central moments of inertia are equal to each other. The linear bending theory for thin inextensible rods is used to describe the deformations. The functionals of elastic and dissipative forces are introduced according to this model. The asymptotic method of motions separation is used to derive the equations of rotational motion reflecting the influence of the fluctuations, caused by the deformations of the rods. The method of motion separation is based on the assumption that the period of the autonomous oscillations of a point belonging to the rod is much smaller than the characteristic time of these oscillations’ decay, which, in its turn, is much smaller than the characteristic time of the system’s motion as a whole. That is why only the oscillations induced by the external and inertial forces are taken into account when deriving the equations of the rotational motion. The perturbed equations are described by a third-order system of ordinary differential equations in the dimensionless variable equal to the ratio of the satellite’s absolute value of angular velocity to the mean motion of the satellite’s center of mass, the angle between the satellite’s axis of symmetry and a fixed axis and the mean anomaly. The right-hand sides of the equation depend on the mean anomaly implicitly through the true anomaly. A new slow angular variable is introduced in order to perform the averaging for the perturbed system near the 3:2 resonance, and the averaging is

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Decca, R. S. "Differential Casimir measurements on an engineered sample: Some experimental details." International Journal of Modern Physics A 31, no. 02n03 (January 20, 2016): 1641024. http://dx.doi.org/10.1142/s0217751x16410244.

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An experimental technique has been recently developed to measure forces differentially between two samples with similar but not identical compositions. The implementation of this approach, with the important reduction in common background effects is reported. An Au-covered rotating sample composed of Au and Ni sectors interacts with either Au-or Ni- covered spheres. Emphasis is paid to the discussion of remnant systematic effects and their impact on the measurements. It is observed that a residual impulsive motion of the axis of rotation of the apparatus remain, contributing at the 0.1 fN level. Apparently random oscillations of the axis of rotation also increase the minimum detectable force by a factor near two. Finally, the remnant magnetic interaction between not completely demagnetized Ni is reduced beyond detection by using a spatial and temporal averaging of the contribution.

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Kajiwara, Hidekazu, and Manabu Aoyagi. "Amplitude and rotational speed control of variable length pendulum by periodic input." Meccanica 56, no. 1 (January 2021): 227–37. http://dx.doi.org/10.1007/s11012-020-01299-8.

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AbstractIn this paper, a control law to stabilize the amplitude or rotational speed of a variable length pendulum to a desired value by periodically changing the position of the center of gravity is proposed. First, the motion of the pendulum oscillating around a lower equilibrium point is analyzed using the averaging method, and a first-order differential equation for the amplitude of the pendulum is derived. Subsequently, using the derived equation of motion, a control law is designed to control the amplitude of the pendulum to the desired value. Similarly, the motion of a pendulum rotating continuously around the rotation axis is analyzed, the first-order differential equation for the angular velocity of the pendulum is derived, and then a control law of the rotational speed is designed. The derived nonlinear feedback control law consists of the amplitude, angle, and angular velocity of the pendulum in the case of amplitude control, and in the case of rotational speed control, the rotational velocity and angular acceleration of the pendulum. Finally, by using the proposed control method, it is shown that the amplitude and rotational speed of the pendulum can be controlled to the desired values.

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Hill, Frank, David M. Rust, and Thierry Appourchaux. "Rotation in the solar convection zone inferred from Fabry-Perot observations of the 5-min oscillations." Symposium - International Astronomical Union 123 (1988): 49–52. http://dx.doi.org/10.1017/s0074180900157717.

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Full disk observations of the 5-min solar oscillations have been obtained with a lithium niobate Fabry-Perot filter. The equatorial solar rotation rate as a function of depth has been inferred from the sectoral modes of oscillation using the Backus-Gilbert optimal averaging inversion method. The results show a rotation rate that slowly decreases over the depths of 15 to 56 Mm below the photosphere. The results are in agreement with the previous Duvall-Harvey observations.

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Kogan, L. R., and N. A. Eysmont. "The requirement to the baseline Knowing of a Space VLBI." International Astronomical Union Colloquium 131 (1991): 115–18. http://dx.doi.org/10.1017/s0252921100013178.

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AbstractIt is shown that the influence of a baseline knowing error on the fringe rate change during coherent averaging time interval is extremely increasing for space VLBI due to more angle velocity of a space baseline rotation comparatively with ground VLBI. It is shown on the example of Radioastron orbit that the reguirement to its orbit for such a short wavelength as 1.35 cm is determined by unknowing of the fringe rate change during coherent averaging time interval rather than by delay ambiguity and this reguirement is equal several meters.

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Mort, Brendan C., and Jochen Autschbach. "Temperature Dependence of the Optical Rotation of Fenchone Calculated by Vibrational Averaging." Journal of Physical Chemistry A 110, no. 40 (October 2006): 11381–83. http://dx.doi.org/10.1021/jp064877h.

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Hill, Frank, Douglas Gough, Juri Toomre, and Deborah A. Haber. "Solar equatorial rotation rate inferred from inversion of frequency splitting of high-degree modes." Symposium - International Astronomical Union 123 (1988): 45–48. http://dx.doi.org/10.1017/s0074180900157705.

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The equatorial rotation rate has been inferred as a function of depth through the outer 16 Mm of the Sun from observations of high-degree five-minute oscillations. An optimal averaging inversion procedure due to Backus & Gilbert (1970) has been applied to frequency splittings measured from power spectra obtained using Doppler data spanning three and five consecutive days. The resulting rotation curves have proven to be much more stable than the curves obtained from data sets of single days. The results imply that the solar rotation rate increases with depth by 0.023 μHz reaching a maximum at about 2 Mm below the surface, then decreases by 0.037 μHz down to 16 Mm.

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Edwards, Linnell, Jack R. Burney, Michael Brimacombe, and Allan H. MacRae. "Potato Land Use and Nitrate Runoff Characteristics of Two Subcatchments of the Wilmot River Watershed, Prince Edward Island (PEI), Canada." Water Quality Research Journal 43, no. 2-3 (May 1, 2008): 121–28. http://dx.doi.org/10.2166/wqrj.2008.015.

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Abstract Two subcatchments in the upper reaches of an arable watershed in central Prince Edward Island (PEI), farmed mostly to potatoes (in rotation), were monitored year-round for nitrate runoff. Land management inventories were done every fall and spring and assessed against nitrate runoff through regression analysis for the period 1991 to 2004. Nitrate concentration (averaging approximately 7 mg L-1 over 14 years) in the outflow varied considerably yearly (standard deviation: 2.76) and monthly (standard deviation: 3.43), and exceeded quality guidelines (of 13 mg L-1) for aquatic life in freshwaters at about a 6% frequency, averaging a nitrate-dollar loss of $1.70 per hectare per year.

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31

Spraggon, Glen. "Envelope skeletonization as a means to determine monomer masks and non-crystallographic symmetry relationships: application in the solution of the structure of fibrinogen fragment D." Acta Crystallographica Section D Biological Crystallography 55, no. 2 (February 1, 1999): 458–63. http://dx.doi.org/10.1107/s0907444998009834.

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An algorithm is described which utilizes the solvent mask generated by the solvent-flattening technique to calculate a monomer molecular envelope. In the case where non-crystallographic symmetry (NCS) is present in the crystal and self-rotation angles are known from a self-rotation function, the resultant monomer envelopes can be used to search for the translation component of the NCS element by a three-dimensional search in real space. In the absence of self-rotation angles, the monomer envelope may be used to derive the NCS operators by reciprocal-space techniques. Thus, an automatic procedure for averaging directly from the solvent-flattening stage can be implemented. The procedure was instrumental in the structure solution of fibrinogen fragment D, which is presented as an example.

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Elnashef, B., and S. Filin. "ROTATION ONLY BUNDLE-ADJUSTMENT FOR THE GENERALIZED CAMERA MODEL AND ITS APPLICATION FOR LARGE-SCALE UNDERWATER IMAGE-SETS." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2022 (May 17, 2022): 325–32. http://dx.doi.org/10.5194/isprs-annals-v-2-2022-325-2022.

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Abstract. The generalized camera model allows handling a broad range of imaging systems for which the common central perspective model no longer applies. While offering greater modeling flexibility, designated orientation procedures need to support its application. In that respect, models that facilitate the computation of the bundle-adjustment solution are imperative as a means to solve the motion and structure of a large set of images. Being non-linear, the bundle adjustment solution requires good initial estimates and the filtering of outlying matches. To facilitate such a solution, we propose in this paper a method for estimating the global rotations of a set of views independent of their translation and the scene structure. This method is then used to improve the robustness, efficiency, and convergence of the solution when used as a refinement to the global rotations. The proposed pipeline is evaluated by experiments on synthetic and real-world data of axial flat-refractive cameras. It shows that the proposed method produces more accurate and optimal initial estimates of the global rotations than the state-of-the-art rotation averaging method.

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LI Jin-peng, 李劲澎, 姜. 挺. JIANG Ting, 龚志辉 GONG Zhi-hui, and 江刚武 JIANG Gang-wu. "GPS-supported 3D reconstruction of UAV images based on robust Lie-algebraic rotation averaging." Optics and Precision Engineering 25, no. 6 (2017): 1607–18. http://dx.doi.org/10.3788/ope.20172506.1607.

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Barabash, R. I., and P. Klimanek. "X-ray scattering by crystals with local lattice rotation fields." Journal of Applied Crystallography 32, no. 6 (December 1, 1999): 1050–59. http://dx.doi.org/10.1107/s0021889899010237.

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X-ray (or neutron) scattering by crystals with local rotation fields arising from dislocations is treated on the basis of the formalism of the kinematical diffraction theory. Such fields mostly change the intensity distribution of reflections in the azimuthal plane. Scattering intensity in the azimuthal plane for crystals with one or two sets of different-type dislocation walls, causing local rotations in the lattice, is analysed. In this case the intensity distribution is close to Lorentzian in the radial direction and to Gaussian in the azimuthal direction. The expressions for the scattering intensity are valid when averaging over a large statistical ensemble of defects. If this condition is not fulfilled, the intensity distribution in the azimuthal plane will split into several spikes. The mean distance between these spikes in the reciprocal-lattice space is connected with the disorientation between the walls. The conditions necessary for such splitting of the reflection into spikes are considered. The values of the limiting disorientation angle for some common scattering volumes and distances between dislocation walls are evaluated.

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35

Nessler, Reed, and Tuguldur Kh Begzjav. "A general method for rotational averages." Journal of Physics: Conference Series 2090, no. 1 (November 1, 2021): 012041. http://dx.doi.org/10.1088/1742-6596/2090/1/012041.

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Abstract The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

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Hanson, Andrew J. "The quaternion-based spatial-coordinate and orientation-frame alignment problems." Acta Crystallographica Section A Foundations and Advances 76, no. 4 (June 18, 2020): 432–57. http://dx.doi.org/10.1107/s2053273320002648.

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The general problem of finding a global rotation that transforms a given set of spatial coordinates and/or orientation frames (the `test' data) into the best possible alignment with a corresponding set (the `reference' data) is reviewed. For 3D point data, this `orthogonal Procrustes problem' is often phrased in terms of minimizing a root-mean-square deviation (RMSD) corresponding to a Euclidean distance measure relating the two sets of matched coordinates. This article focuses on quaternion eigensystem methods that have been exploited to solve this problem for at least five decades in several different bodies of scientific literature, where they were discovered independently. While numerical methods for the eigenvalue solutions dominate much of this literature, it has long been realized that the quaternion-based RMSD optimization problem can also be solved using exact algebraic expressions based on the form of the quartic equation solution published by Cardano in 1545; focusing on these exact solutions exposes the structure of the entire eigensystem for the traditional 3D spatial-alignment problem. The structure of the less-studied orientation-data context is then explored, investigating how quaternion methods can be extended to solve the corresponding 3D quaternion orientation-frame alignment (QFA) problem, noting the interesting equivalence of this problem to the rotation-averaging problem, which also has been the subject of independent literature threads. The article concludes with a brief discussion of the combined 3D translation–orientation data alignment problem. Appendices are devoted to a tutorial on quaternion frames, a related quaternion technique for extracting quaternions from rotation matrices and a review of quaternion rotation-averaging methods relevant to the orientation-frame alignment problem. The supporting information covers novel extensions of quaternion methods to the 4D Euclidean spatial-coordinate alignment and 4D orientation-frame alignment problems, some miscellaneous topics, and additional details of the quartic algebraic eigenvalue problem.

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37

Fallahi, Bita, Ron Sloboda, Nawaid Usmani, and Mahdi Tavakoli. "Model Averaging and Input Transformation for 3D Needle Steering." Journal of Medical Robotics Research 03, no. 03n04 (September 2018): 1841004. http://dx.doi.org/10.1142/s2424905x18410040.

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In this paper, a duty-cycle-based method is proposed for needle steering in 3D. The paper models the continuous 3D needle steering problem as a four-mode switching system and provides a new average-based formulation to transform the continuous input into a switching sequence. In this structure, the needle tip deflection control system is decomposed to two different 2D subsystems. Each subsystem has its own input, for which a controller can be designed to adjust a switching duty cycle. The duty cycles from the two subsystems are then combined to provide an axial needle rotation command to control the needle deflection in 3D. In order to show the application of the proposed formulation, robust sliding mode technique is employed to design controllers for each subsystem and, thus for the total system in 3D. The controllers are designed to be robust with respect to uncertainties in the value of the needle path curvature and to deal with measurement limitations. The performance of the proposed framework is shown by performing experiments in different scenarios.

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38

Васильев, И. А., О. М. Кущенко, С. С. Рудый, and Ю. В. Рождественский. "Эффективный ротационный потенциал молекулярных ионов в плоской радиочастотной ловушке." Журнал технической физики 89, no. 9 (2019): 1457. http://dx.doi.org/10.21883/jtf.2019.09.48074.422-18.

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In the present article we first described the concept of effective rotation potential (ERP) – the analog of well-known pseudopotential for the case of a charged diatomic particle model localization in the 2D quadrupole RF trap. We have shown that ERP can be used for describing dynamic of wide range specific charged diatomic-like particles with separate centers of masses and charges. We have compared the result of pseudopotential-averaging for single ion localization and ERP-averaging for diatomic-like charge structure and obtained additional quasi-equilibrium points both for the center of masses motion (COM) and for angle orientation. The additional quasi-equilibrium points strongly influence on dynamics and mass-selective characteristics of diatomic-like charge structure at the case of localization in a quadrupole ion trap.

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39

VOROBIEFF, PETER, and ROBERT E. ECKE. "Turbulent rotating convection: an experimental study." Journal of Fluid Mechanics 458 (May 10, 2002): 191–218. http://dx.doi.org/10.1017/s0022112002007814.

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We present experimental measurements of velocity and temperature fields in horizontal planes crossing a cylindrical Rayleigh–Bénard convection cell in steady rotation about its vertical axis. The range of dimensionless rotation rates Ω is from zero to 5×104 for a Rayleigh number R = 3.2×108. The corresponding range of convective Rossby numbers is ∞ > Ro > 0.06. The patterns of velocity and temperature and the flow statistics characterize three basic flow regimes. For Ro [Gt ] 1, the flow is dominated by vortex sheets (plumes) typical of turbulent convection without rotation. The flow patterns for Ro ∼ 1 are cyclone-dominated, with anticyclonic vortices rare. As the Rossby number continues to decrease, the number of anticyclonic vortex structures begins to grow but the vorticity PDF in the vicinity of the top boundary layer still shows skewness favouring cyclonic vorticity. Velocity-averaging near the top of the cell suggests the existence of a global circulation pattern for Ro [Gt ] 1.

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Heiderscheit, Bryan C., Joseph Hamill, and Richard E. A. van Emmerik. "Variability of Stride Characteristics and Joint Coordination among Individuals with Unilateral Patellofemoral Pain." Journal of Applied Biomechanics 18, no. 2 (May 2002): 110–21. http://dx.doi.org/10.1123/jab.18.2.110.

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The purpose of this investigation was to determine whether individuals with patellofemoral pain (PFP) display a reduction in intralimb joint coordination variability compared to nonimpaired persons. In addition, it was hypothesized that the variability of the stride characteristics would be similar between groups. Eight individuals with unilateral PFP and 8 nonimpaired participants ran on a treadmill at a fixed (2.68 m·s–1) and preferred speed while stride characteristics and 3-D kinematics of the bilateral lower extremities were recorded. Intralimb coordination variability was measured using a vector coding technique applied to relative motion plots of various joint couplings. The PFP group displayed greater stride length variability during running at the preferred speed. However, this was not the case during running at the fixed speed. When averaging across the entire stride cycle, coordination variability for all joint couplings was consistent between the two groups. However, further analysis about heel-strike revealed reduced joint coordination variability for the thigh rotation/leg rotation coupling of the PFP group’s injured limb compared to that of the nonimpaired group. With the exception of the transverse plane rotations at heel-strike, it would appear that the level of pain experienced by the PFP participants may not be great enough to produce a change in the intralimb coordination patterns during running.

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41

Zhang Yanwei, 张艳微, 苏东奇 Su Dongqi, 隋永新 Sui Yongxin, and 杨怀江 Yang Huaijiang. "Absolute Testing of Rotationally Asymmetric Surface Deviation with the Method of Rotation-Averaging and Compensation." Chinese Journal of Lasers 41, no. 7 (2014): 0708007. http://dx.doi.org/10.3788/cjl201441.0708007.

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42

Finnigan, J. J., R. Clement, Y. Malhi, R. Leuning, and H. A. Cleugh. "A Re-Evaluation of Long-Term Flux Measurement Techniques Part I: Averaging and Coordinate Rotation." Boundary-Layer Meteorology 107, no. 1 (April 2003): 1–48. http://dx.doi.org/10.1023/a:1021554900225.

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43

Mort, Brendan C., and Jochen Autschbach. "Temperature Dependence of the Optical Rotation in Six Bicyclic Organic Molecules Calculated by Vibrational Averaging." ChemPhysChem 8, no. 4 (March 12, 2007): 605–16. http://dx.doi.org/10.1002/cphc.200600757.

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44

STEWART, ANDREW L., and PAUL J. DELLAR. "Multilayer shallow water equations with complete Coriolis force. Part 1. Derivation on a non-traditional beta-plane." Journal of Fluid Mechanics 651 (March 24, 2010): 387–413. http://dx.doi.org/10.1017/s0022112009993922.

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We derive equations to describe the flow of multiple superposed layers of inviscid, incompressible fluids with constant densities over prescribed topography in a rotating frame. Motivated by geophysical applications, these equations incorporate the complete Coriolis force. We do not make the widely used ‘traditional approximation’ that omits the contribution to the Coriolis force from the locally horizontal part of the rotation vector. Our derivation is performed by averaging the governing Euler equations over each layer, and from two different forms of Hamilton's variational principle that differ in their treatment of the coupling between layers. The coupling may be included implicitly through the map from Lagrangian particle labels to particle coordinates, or explicitly by adding terms representing the work done on each layer by the pressure exerted by the layers above. The latter approach requires additional terms in the Lagrangian, but extends more easily to many layers. We show that our equations obey the expected conservation laws for energy, momentum and potential vorticity. The conserved momentum and potential vorticity are modified by non-traditional effects. The vertical component of the rotation vector that appears in the potential vorticity for each layer under the traditional approximation is replaced by the component perpendicular to the layer's midsurface. The momentum includes an additional contribution that reflects changes in angular momentum caused by changes in a fluid element's distance from the rotation axis as it is displaced vertically. Again, this effect is absent in the traditional approximation.

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45

Edwards, Linnell, G. Richter, B. Bernsdorf, R. G. Schmidt, and J. Burney. "Measurement of rill erosion by snowmelt on potato fields under rotation in Prince Edward Island (Canada)." Canadian Journal of Soil Science 78, no. 3 (August 1, 1998): 449–58. http://dx.doi.org/10.4141/s97-053.

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Cool-period soil erosion from farmland in Prince Edward Island occurs predominantly through rilling mainly due to snowmelt. This is mostly evident on fields coming out of potatoes (Solanum tuberosum L.), a crop that is traditionally cultivated as part of a 2-yr rotation with cereal grains, or a 3-yr rotation with cereal grains and a forage crop for hay. Accurate assessment of snowmelt erosion (associated processes and effects) has been historically constrained by data inadequacy, particularly for rilling; and although a number of models have now been developed for estimating cool-period erosion, they still stand to benefit from the generation of actual field data. In the present study, actual volume measurements were made of erosion forms, for about 80 site-years, after the spring snowmelt in fields at various stages of potato rotation. Cool-period erosion, predominantly rills, amounted to about 30 t ha−1 for 2-yr and 3-yr rotations, thus an annual seasonal average of 15 t ha−1 and 10 t ha−1, respectively. Potato fields left untilled over winter averaged about 20 t ha–1 which increased to 36 t ha−1 with fall ploughing. Sediment deposition in fields coming out of potatoes was 13.3 t ha−1 compared with the amount of 0.4 t ha−1 in fields coming out of forages and 1.6 t ha−1 in fields coming out of grain. Fields going into the winter in sod or stubble showed negligible erosion, averaging about 0.1 t ha−1 in spring. The results of this study demonstrate the dominant influence of cropping practice in the erosion process during the cool period, and the tendency for traditional computational procedures to underestimate soil loss. Key words: Cool-period erosion, rilling, rill volume, sediment deposition, soil-loss prediction, erosion mapping, crop rotation

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46

Gao, Chong-yi, Guo-jun Du, Yan Feng, and Jian-xiong Li. "Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/216197.

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According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.

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47

Reich, M., and C. Heipke. "CONVEX IMAGE ORIENTATION FROM RELATIVE ORIENTATIONS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-3 (June 3, 2016): 107–14. http://dx.doi.org/10.5194/isprsannals-iii-3-107-2016.

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In this paper we propose a novel workflow for the estimation of global image orientations given relative orientations between pairs of overlapping images. Our approach is convex and independent on initial values. First, global rotations are estimated in a relaxed semidefinite program (SDP) and refined in an iterative least squares adjustment in the tangent space of SO(3). A critical aspect is the handling of outliers in the relative orientations. We present a novel heuristic graph based approach for filtering the relative rotations that outperforms state-of-the-art robust rotation averaging algorithms. In a second part we make use of point-observations, tracked over a set of overlapping images and formulate a linear homogeneous system of equations to transfer the scale information between triplets of images, using estimated global rotations and relative translation directions. The final step consists of refining the orientation parameters in a robust bundle adjustment. The proposed approach handles outliers in the homologous points and relative orientations in every step of the processing chain. We demonstrate the robustness of the procedure on synthetic data. Moreover, the performance of our approach is illustrated on real world benchmark data.

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Reich, M., and C. Heipke. "CONVEX IMAGE ORIENTATION FROM RELATIVE ORIENTATIONS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences III-3 (June 3, 2016): 107–14. http://dx.doi.org/10.5194/isprs-annals-iii-3-107-2016.

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In this paper we propose a novel workflow for the estimation of global image orientations given relative orientations between pairs of overlapping images. Our approach is convex and independent on initial values. First, global rotations are estimated in a relaxed semidefinite program (SDP) and refined in an iterative least squares adjustment in the tangent space of SO(3). A critical aspect is the handling of outliers in the relative orientations. We present a novel heuristic graph based approach for filtering the relative rotations that outperforms state-of-the-art robust rotation averaging algorithms. In a second part we make use of point-observations, tracked over a set of overlapping images and formulate a linear homogeneous system of equations to transfer the scale information between triplets of images, using estimated global rotations and relative translation directions. The final step consists of refining the orientation parameters in a robust bundle adjustment. The proposed approach handles outliers in the homologous points and relative orientations in every step of the processing chain. We demonstrate the robustness of the procedure on synthetic data. Moreover, the performance of our approach is illustrated on real world benchmark data.

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Fukano, Mako, Yuji Kuroyanagi, Toru Fukubayashi, and Scott Banks. "Three-Dimensional Kinematics of the Talocrural and Subtalar Joints During Drop Landing." Journal of Applied Biomechanics 30, no. 1 (February 2014): 160–65. http://dx.doi.org/10.1123/jab.2012-0192.

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The bones and soft tissues of the foot act as a shock attenuator and the relative bony motions of the talocrural and subtalar joints are the subject of research interest for their roles in lower extremity pathology. Despite this interest, little information exists on the precise in vivo talocrural and subtalar joint kinematics during dynamic activities. Therefore, the purpose of this study was to quantify the three-dimensional kinematics of the talocrural and subtalar joints during landing by using single-plane fluoroscopic imaging and shape matching techniques. Three-dimensional bone positions for 6 subjects during landing from a 10 cm height were determined by using 3D-2D model-image registration techniques. The primary talocrural joint motion after toe contact was dorsiflexion with rotation ranges averaging 12° ± 7° dorsiflexion, 2° ± 2° eversion, and 3° ± 2° internal rotation. The subtalar joint exhibited similar patterns of increased dorsiflexion, eversion, and external rotation up to 150 ms after landing. The angular changes were 5° ± 3° dorsiflexion, 7° ± 3° eversion, and 6° ± 2° external rotation. This study contributes to the quantitative understanding of the function of the normal talocrural and subtalar joints and can be used for comparison with data obtained from injured feet.

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Podvigina, O. M. "Rotation of a Planet in a Three-body System: a Non-resonant Case." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221001.

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We investigate the temporal evolution of the rotation axis of a planet in a system comprised of the planet (which we call an exo-Earth), a star (an exo-Sun) and a satellite (an exo-Moon). The planet is assumed to be rigid and almost spherical, the difference between the largest and the smallest principal moments of inertia being a small parameter of the problem. The orbit of the planet around the star is a Keplerian ellipse. The orbit of the satellite is a Keplerian ellipse with a constant inclination to the ecliptic, involved in two types of slow precessional motion, nodal and apsidal. Applying time averaging over the fast variables associated with the frequencies of the motion of exo-Earth and exo-Moon, we obtain Hamilton’s equations for the evolution of the angular momentum axis of the exo-Earth. Using a canonical change of variables, we show that the equations are integrable. Assuming that the exo-Earth is axially symmetric and its symmetry and rotation axes coincide, we identify possible types of motions of the vector of angular momentum on the celestial sphere. Also, we calculate the range of the nutation angle as a function of the initial conditions. (By the range of the nutation angle we mean the difference between its maximal and minimal values.)

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Journal articles on the topic 'Rotation averaging'

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