Academic literature on the topic 'Known-rotation problem'
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Journal articles on the topic "Known-rotation problem"
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Lian, Yong-sheng, Jun-yi Sun, Zhi-xin Yang, Xiao-ting He, and Zhou-lian Zheng. "Closed-form solution of well-known Hencky problem without small-rotation-angle assumption." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96, no. 12 (May 27, 2016): 1434–41. http://dx.doi.org/10.1002/zamm.201600059.
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Stebulyanin, M. M., and Ya I. Pimushkin. "Solution of the Rodriguez Equation in Modeling Volumetric Geometric Accuracy of Multi-Coordinate Systems." EPJ Web of Conferences 248 (2021): 04004. http://dx.doi.org/10.1051/epjconf/202124804004.
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The article describes the solution to the Rodrigues equation for determining the volumetric accuracy of multi-axis CNC-controlled systems. An algorithm for calculating the position of the axis of a rotary kinematic pair in problems of volumetric accuracy of mechanical motion of a portal-type system with an additional pair of rotation. The algorithm is based on the analytical solution of the Rodrigues equation in the inverse problem of finding the vector of the final rotation of the known modulus from the known initial and final values of the characteristic vector of the rotated rigid body. In contrast to the well-known direct problem, where based on a finite rotation vector known in direction and magnitude, and the initial value of the characteristic vector of a body, its final value is found, the inverse problem of the Rodrigues equation is not that common due to the nonlinearity and need to solve a nonlinear coupled system of second order equations. The results of this work make it possible to expand the dimension of the space of generalized coordinates of the system analyzed for the volumetric accuracy from three to four. This is expected contribute to the development of ultra-precise systems of controlled mechanical movement. The analytical results of this study were verified by comparing with numerical solutions of the inverse problem in Maple.
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Lian, Yong-sheng, Xiao-ting He, Guang-hui Liu, Jun-yi Sun, and Zhou-lian Zheng. "Application of perturbation idea to well-known Hencky problem: A perturbation solution without small-rotation-angle assumption." Mechanics Research Communications 83 (July 2017): 32–46. http://dx.doi.org/10.1016/j.mechrescom.2017.05.001.
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DALZIEL, STUART B. "The twists and turns of rotating turbulence." Journal of Fluid Mechanics 666 (January 6, 2011): 1–4. http://dx.doi.org/10.1017/s0022112010005409.
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Turbulence is widely considered one of the most important and most difficult unsolved problems in classical physics. It is also the area of fluid mechanics where the greatest effort is exerted, the most papers published and, some would argue, the least progress made. Although direct numerical simulation is becoming an increasingly valuable tool, there remains a need for high-quality experiments to underpin our theoretical and numerical progress. Such statements apply equally to the ‘classical’ problem of homogeneous isotropic turbulence and to turbulence in its many other guises. Of particular interest is turbulence in a rotating system, where it is well known that the influence of rotation leads to the development of anisotropy and the elongation of scales parallel to the rotation axis. Moisy et al. (J. Fluid Mech., 2010, this issue, vol. 666, pp. 5–35) present new experiments in the free decay of grid-generated turbulence in a rotating system. They investigate the emergence of anisotropy from essentially isotropic initial conditions. While it is well known that rotation suppresses velocity gradients parallel to the rotation axis, Moisy et al. (2010) uncover some startling and previously overlooked implications.
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Martin, John, Stefan Weigert, and Olivier Giraud. "Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States." Quantum 4 (June 22, 2020): 285. http://dx.doi.org/10.22331/q-2020-06-22-285.
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Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.
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MATTHEWS, PAUL, and STEPHEN COX. "Linear stability of rotating convection in an imposed shear flow." Journal of Fluid Mechanics 350 (November 10, 1997): 271–93. http://dx.doi.org/10.1017/s0022112097006903.
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In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.
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Lian, Yong-Sheng, Jun-Yi Sun, Zhi-Hang Zhao, Xiao-Ting He, and Zhou-Lian Zheng. "A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations." Mathematics 8, no. 4 (April 20, 2020): 631. http://dx.doi.org/10.3390/math8040631.
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In this paper, the well-known Föppl–Hencky membrane problem—that is, the problem of axisymmetric deformation of a transversely uniformly loaded and peripherally fixed circular membrane—was resolved, and a more refined closed-form solution of the problem was presented, where the so-called small rotation angle assumption of the membrane was given up. In particular, a more effective geometric equation was, for the first time, established to replace the classic one, and finally the resulting new boundary value problem due to the improvement of geometric equation was successfully solved by the power series method. The conducted numerical example indicates that the closed-form solution presented in this study has higher computational accuracy in comparison with the existing solutions of the well-known Föppl–Hencky membrane problem. In addition, some important issues were discussed, such as the difference between membrane problems and thin plate problems, reasonable approximation or assumption during establishing geometric equations, and the contribution of reducing approximations or relaxing assumptions to the improvement of the computational accuracy and applicability of a solution. Finally, some opinions on the follow-up work for the well-known Föppl–Hencky membrane were presented.
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HILLS, CHRISTOPHER P., and H. K. MOFFATT. "Rotary honing: a variant of the Taylor paint-scraper problem." Journal of Fluid Mechanics 418 (September 10, 2000): 119–35. http://dx.doi.org/10.1017/s0022112000001075.
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The three-dimensional flow in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the ‘Taylor’ streamlines of the well-known ‘paint-scraper’ problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honed by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows.
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Glybovets, M. M., N. M. Gulayeva, and I. O. Morozov. "Analysis of Genetic Algorithms for solving the 2D Orthogonal Strip Packing Problem." PROBLEMS IN PROGRAMMING, no. 4 (December 2016): 104–16. http://dx.doi.org/10.15407/pp2016.04.104.
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A class of genetic algorithms for solving the 2D Strip Packing Problem is investigated. The theoretical analysis of the complexity of implementing decoders MERA and BLF is done. Original implementations of these MERA and BLF decoders enhanced with a number of heuristic optimizations are proposed. Genetic algorithm for solving the 2D Strip Packing Problem for special cases (allowed/forbidden objects rotation by 90°) with the use of MERA/BLF decoders is proposed. Extensive computational experiments with well-known instances are performed to analyze different configurations of basic parameters of proposed genetic algorithm. The comparison of the obtained algorithm with other known algorithms is given.
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Ziegler, Franz, and Piotr Borejko. "The Method of Generalized Ray-Revisited." Journal of Mechanics 16, no. 2 (June 2000): 125–26. http://dx.doi.org/10.1017/s1727719100001696.
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In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force poses an axisymmetric problem which is compatible with the Fourier transformation applied to the coordinates in the horizontal plane.
Dissertations / Theses on the topic "Known-rotation problem"
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Zhang, Qianggong. "Robust and large-scale quasiconvex programming in structure-from-motion." Thesis, 2018. http://hdl.handle.net/2440/114269.
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Structure-from-Motion (SfM) is a cornerstone of computer vision. Briefly speaking,
SfM is the task of simultaneously estimating the poses of the cameras behind a set of images of a
scene, and the 3D coordinates of the points in the scene.
Often, the optimisation problems that underpin SfM do not have closed-form solutions, and finding
solutions via numerical schemes is necessary. An objective function, which measures the discrepancy
of a geometric object (e.g., camera poses, rotations, 3D coordi- nates) with a set of image
measurements, is to be minimised. Each image measurement gives rise to an error function. For
example, the reprojection error, which measures the distance between an observed image point and
the projection of a 3D point onto the image, is a commonly used error function.
An influential optimisation paradigm in SfM is the ℓ₀₀ paradigm, where the objective function takes
the form of the maximum of all individual error functions (e.g. individual reprojection errors of
scene points). The benefit of the ℓ₀₀ paradigm is that the objective function of many SfM
optimisation problems become quasiconvex, hence there is a unique minimum in the objective
function. The task of formulating and minimising quasiconvex objective functions is called
quasiconvex programming.
Although tremendous progress in SfM techniques under the ℓ₀₀ paradigm has been made, there are still
unsatisfactorily solved problems, specifically, problems associated with large-scale input data and
outliers in the data. This thesis describes novel techniques to
tackle these problems.
A major weakness of the ℓ₀₀ paradigm is its susceptibility to outliers. This thesis improves the
robustness of ℓ₀₀ solutions against outliers by employing the least median of squares (LMS)
criterion, which amounts to minimising the median error. In the context of triangulation, this
thesis proposes a locally convergent robust algorithm underpinned by a novel quasiconvex plane
sweep technique. Imposing the LMS criterion achieves significant outlier tolerance, and, at the
same time, some properties of quasiconvexity greatly simplify the process of solving the LMS
problem.
Approximation is a commonly used technique to tackle large-scale input data. This thesis introduces
the coreset technique to quasiconvex programming problems. The coreset technique aims find a
representative subset of the input data, such that solving the same problem on the subset yields a
solution that is within known bound of the optimal solution on the complete input set. In
particular, this thesis develops a coreset approximate algorithm to handle large-scale
triangulation tasks.
Another technique to handle large-scale input data is to break the optimisation into multiple
smaller sub-problems. Such a decomposition usually speeds up the overall optimisation process,
and alleviates the limitation on memory. This thesis develops a large-scale optimisation algorithm
for the known rotation problem (KRot). The proposed method decomposes the original quasiconvex
programming problem with potentially hundreds of thousands of parameters into multiple sub-problems
with only three parameters each. An efficient solver based on a novel minimum enclosing ball
technique is proposed to solve the sub-problems.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Computer Science, 2018
Book chapters on the topic "Known-rotation problem"
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dos Santos, Lana, Marcos Arenales, Alysson Costa, and Ricardo Santos. "A Linear Optimization Approach for Increasing Sustainability in Vegetable Crop Production." In Green Technologies, 236–67. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-472-1.ch204.
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This chapter is concerned with a set of optimization problems associated to crop rotation scheduling in the context of vegetable crop production according to some ecological criteria: no crop of the same botanic family is planted in sequence, green manure and fallow periods must be present in any schedule. A core mathematical model called the crop rotation scheduling model is proposed to represent these ecological criteria together with specific technical constraints associated to the growing of vegetable crops. Three optimization problems based on crop rotation schedules are written in detail in this chapter. For each problem, the authors present a general modeling framework and a solution methodology based on a technique known as column generation, which iteratively builds crop rotation plans for a number of plots. Some extensions are also presented, with the aim of incorporating additional characteristics found in production field conditions. This chapter ends with a brief discussion on a set of computational experiments and some suggestions for future research.
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dos Santos, Lana, Marcos Arenales, Alysson Costa, and Ricardo Santos. "A Linear Optimization Approach for Increasing Sustainability in Vegetable Crop Production." In Computational Methods for Agricultural Research, 234–65. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-61692-871-1.ch012.
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This chapter is concerned with a set of optimization problems associated to crop rotation scheduling in the context of vegetable crop production according to some ecological criteria: no crop of the same botanic family is planted in sequence, green manure and fallow periods must be present in any schedule. A core mathematical model called the crop rotation scheduling model is proposed to represent these ecological criteria together with specific technical constraints associated to the growing of vegetable crops. Three optimization problems based on crop rotation schedules are written in detail in this chapter. For each problem, the authors present a general modeling framework and a solution methodology based on a technique known as column generation, which iteratively builds crop rotation plans for a number of plots. Some extensions are also presented, with the aim of incorporating additional characteristics found in production field conditions. This chapter ends with a brief discussion on a set of computational experiments and some suggestions for future research.
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Kaliyeva, Kulyash. "Energy Conservation Law for the Turbulent Motion in the Free Atmosphere." In Advances in Systems Analysis, Software Engineering, and High Performance Computing, 105–38. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-8823-0.ch003.
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This chapter presents convergent-divergent flow in the free atmosphere which is governed by the three dimensional Navier-Stokes equations and deals with the fundamental problem of fluid dynamics. Considering air movement under influence divergence and rotation were found the true dependencies between the velocity vector and the pressure distribution. Following the classical procedure by using rotor operator and a well-known formula of vector analysis were obtained the second kind nonlinear Volterra-Fredholm integral equations in a matrix form which contained only three components of the velocity vector. According to the theory of the matrix operators were defined the velocity components by the successive approximation method. According to the obtained balance equation for the pressure distribution were defined significant properties of the transient convergent-divergent flow which provide a description of the constitutive relationships between three physical quantities: the velocity vector, the external and internal forces, the pressure distribution.
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Steel, Duncan G. "Angular Momentum and the Quantum Gyroscope: The Emergence of Spin." In Introduction to Quantum Nanotechnology, 160–80. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895073.003.0010.
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Continuing with understanding the implications of the postulates in Chapter 7 and following the approach in Chapter 8 to use operators find solutions to the time independent Schrödinger equation, we return to the subject of angular momentum, of importance to many problems including the quantum gyroscope. Aside from playing a central role in any spherically symmetric quantum system, it plays a central role in inertial guidance systems from airplanes and rockets to autonomous vehicles. Working with only the operators of the angular momentum vector, L^=L^xx̌+L^yy̌+L^zž and L^2 and the corresponding commutation relations, a procedure similar to that used in Chapter 8 for the nano-vibrator is used to completely identify the eigenvectors and eigenvalues. However, in Chapter 6, we required that the magnetic quantum number, m where L^z|l.m〉=mℏ|l.m〉, be integer, because the eigenfunction Yl,m(l,m)∝eimϕ, and we required that a full rotation around the z-axis give the same result requiring, eimϕ=eim(ϕ+2π). In the operator approach, there is no such requirement, but there is still a constraint on m, namely that m is either integer or half integer. The requirements in Chapter 6 hold, so what is the meaning of half-integer? This was one of the first results to indicate the existence of intrinsic (not associated with real space rotation) angular moment known as spin.
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Zhou, Jiarui, Junshan Yang, Ling Lin, Zexuan Zhu, and Zhen Ji. "Local Best Particle Swarm Optimization Using Crown Jewel Defense Strategy." In Critical Developments and Applications of Swarm Intelligence, 27–52. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5134-8.ch002.
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Particle swarm optimization (PSO) is a swarm intelligence algorithm well known for its simplicity and high efficiency on various problems. Conventional PSO suffers from premature convergence due to the rapid convergence speed and lack of population diversity. It is easy to get trapped in local optima. For this reason, improvements are made to detect stagnation during the optimization and reactivate the swarm to search towards the global optimum. This chapter imposes the reflecting bound-handling scheme and von Neumann topology on PSO to increase the population diversity. A novel crown jewel defense (CJD) strategy is introduced to restart the swarm when it is trapped in a local optimum region. The resultant algorithm named LCJDPSO-rfl is tested on a group of unimodal and multimodal benchmark functions with rotation and shifting. Experimental results suggest that the LCJDPSO-rfl outperforms state-of-the-art PSO variants on most of the functions.
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Oreskes, Naomi. "Drift Mechanisms in the 1920s." In The Rejection of Continental Drift. Oxford University Press, 1999. http://dx.doi.org/10.1093/oso/9780195117325.003.0010.
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The final chapter of the third edition of The Origin of Continents and Oceans was devoted to the dynamic causes of drift, and Wegener’s tone in these final fifteen pages was decidedly more tentative than in the rest. Frankly acknowledging the huge uncertainties surrounding this issue, he proceeded on the basis of a phenomenological argument. Mountains, Wegener pointed out, are not randomly distributed: they are concentrated on the western and equatorial margins of continents. The Andes and Rockies, for example, trace the western margins of North and South America; the Alps and the Himalayas follow a latitudinal trend on their equatorial sides of Europe and Asia. If mountains are the result of compression on the leading edges of drifting continents, then the overall direction of continental drift must be westward and equatorial. Continental displacements are not random, as the English word drift might imply, but coherent. This coherence had been the inspiration for an earlier version of drift proposed by the American geologist Frank Bursley Taylor (1860–1938). A geologist in the Glacial Division of the U.S. Geological Survey under T. C. Chamberlin, Taylor was primaril known for his work on the Pleistocene geology of the Great Lakes region. But his knowledge extended beyond regional studies: as a special student at Harvard, he had studied geology and astronomy; as a survey geologist under the influence of Chamberlin and G. K. Gilbert, he had published a number of articles on theoretical problems. One of these was an 1898 pamphlet outlining a theory of the origin of the moon by planetary capture; in 1903, Taylor developed his theoretical ideas more fully in a privately published book. Turning the Darwin–Fisher fissiparturition hypothesis on its head, Taylor proposed that the moon had not come from the earth but had been captured by it after the close approach of a cornet. Once caught, (lie tidal effect of the moon increased the speed of the earth’s rotation and pulled the continents away from the poles toward the equator. In 1910, Taylor pursued the geological implications of this idea in an article in the Bulletin of the Geological Society of America entitled “Bearing of the Tertiary Mountain Belt on the Origin of the Earth’s Plan.”
Conference papers on the topic "Known-rotation problem"
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Zhang, Qianggong, Tat-Jun Chin, and Huu Minh Le. "A Fast Resection-Intersection Method for the Known Rotation Problem." In 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2018. http://dx.doi.org/10.1109/cvpr.2018.00318.
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Sweeney, Chris, John Flynn, and Matthew Turk. "Solving for Relative Pose with a Partially Known Rotation is a Quadratic Eigenvalue Problem." In 2014 2nd International Conference on 3D Vision (3DV). IEEE, 2014. http://dx.doi.org/10.1109/3dv.2014.66.
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Higuchi, Hiroshi, and Toshiro Kiura. "Flow-Structure Interaction Problem of a Pitched Baseball Without Spin (Knuckleball)." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30397.
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The “knuckleball” effect is believed to be caused by asymmetric flow separation over the baseball, but little is known about its flow physics. The baseball is gripped with the knuckles in a certain position and is pitched in a way that introduces nearly no rotation, resulting in erratic flight paths which confuse batters. In the experiment described in this paper, the flow near the seams of the baseball is visualized thoroughly and the velocity vector fields near the surface and in the wake are obtained with Digital Particle Image Velocimetry. Depending on its position, the seam is found to trigger the boundary layer transition thus delaying the separation, or to cause separation itself. Three-dimensional wake patterns associated with specific ball orientations are identified and related to the force variations on the ball.
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Guilherme, Karen de Lolo, Jose´ Manoel Balthazar, Paulo Roberto Gardel Kurka, and Masayoshi Tsuchida. "An Overview on a Nonideal System With Three and a Half Degrees of Freedom." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85426.
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The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor.
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Ghosh, S., and D. Roy. "A Family of Runge-Kutta Based Explicit Methods for Rotational Dynamics." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41396.
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The present paper develops a family of explicit algorithms for rotational dynamics and presents their comparison with several existing methods. For rotational motion the configuration space is a non-linear manifold, not a Euclidean vector space. As a consequence the rotation vector and its time derivatives correspond to different tangent spaces of rotation manifold at different time instants. This renders the usual integration algorithms for Euclidean space inapplicable for rotation. In the present algorithms this problem is circumvented by relating the equation of motion to a particular tangent space. It has been accomplished with the help of already existing relation between rotation increments which belongs to two different tangent spaces. The suggested method could in principle make any integration algorithm on Euclidean space, applicable to rotation. However, the present paper is restricted only within explicit Runge-Kutta enabled to handle rotation. The algorithms developed here are explicit and hence computationally cheaper than implicit methods. Moreover, they appear to have much higher local accuracy and hence accurate in predicting any constants of motion for reasonably longer time. The numerical results for solutions as well as constants of motion, indicate superior performance by most of our algorithms, when compared to some of the currently known algorithms, namely ALGO-C1, STW, LIEMID[EA], MCG, SUBCYC-M.
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Serebriakov, Nikolay, and Alexander Selivanov. "Searching for the Optimal Arrangement of Mistuned Blades Based on Solving the Traveling Salesman Problem for Simple Mass-Spring Linear System." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59927.
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Abstract The article presents an approach to finding the optimal arrangement of blades in a bladed disk based on solving the traveling salesman problem using the ant colony algorithm. The solution to the problem is presented for an equivalent model of the bladed disk. The mistuning parameters are assumed as known — for example, from the data of geometric measurements for each blade from the set used for assembling the bladed disk — considering the influence of the rotation on the investigated resonance mode. Approaches have already been published for the construction of equivalent models and the use of combinatorial optimization methods, including solving the traveling salesman problem, to find the optimal arrangement of the blades. Therefore, this article focuses on demonstrating a simple program implementation of this method. This approach allows a quick assessment of the effect of the blade assembly in the bladed disk on the amplitudes of alternating stresses. It even considers several restarts of the algorithm to determine other possible configurations of the system.
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Jakoby, Ralf, Soksik Kim, and Sigmar Wittig. "Correlations of the Convective Heat Transfer in Annular Channels With Rotating Inner Cylinder." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-097.
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In the internal air system of gas turbine engines or generators, a large variety of different types of annular channels with rotating cylinders are found. Even though the geometry is very simple, the flow field in such channels can be completely three-dimensional and also unsteady. From the literature it is well-known, that the basic two-dimensional flow field breaks up into a pattern of counter-rotating vortices, as soon as the critical speed of the inner cylinder is exceeded. The presence of a superimposed axial flow leads to a helical shape of the vortex pairs, which are moving through the channel. For the designer of cooling air systems there are several open questions. Does the formation of a Taylor-vortex flow field significantly affect the convective heat transfer behaviour of the channel flow? Is there a stability problem even for high axial Reynolds-numbers and where is the location of the stability boundary? After all, the general influence of rotation on the heat transfer characteristics has to be known. By the results of flow field and heat transfer measurements, the impact of rotation and the additional influence of Taylor-vortex formation on the heat transfer characteristics in annular channels with axial throughflow will be discussed. The flow field was investigated by time-dependant LDA-measurements, which revealed detailed information about the flow conditions. By a spectral analysis of the measured data, the different flow regimes could be identified. Based on these results, the heat transfer from the hot gas to the rotating inner shaft was determined with a steady-state method. Thus, the influence of the different physical phenomena such as rotation with and without Taylor-vortex formation or the flow development could be separated and quantified. Finally, correlations of the measured results were derived for technical applications.
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Lin, Chung-Yen, and Masayoshi Tomizuka. "Estimating Rigid Transformation With Correlated Observations." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9672.
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The problem of finding the rotation and the translation between two sets of corresponded points is known as the rigid transformation estimation problem. It plays a crucial role in many robotic applications such as “simultaneous localization and mapping” (SLAM), surface reconstruction, and inertial sensor calibration. The most widely used solution to this problem is based on performing the singular value decomposition (SVD) over a derived data matrix. A drawback of the SVD method is that it is a least-squares method and thus may fail to take into account the anisotropic and/or correlated noises, which often present in practical applications. A natural variation is to add a matrix weight to the least-squares problem to balance the estimation errors in different measurement directions. However, it becomes difficult to write down a closed form solution in this setup. In this paper, an efficient algorithm is presented to estimate the rigid transformation with correlated observations. The effectiveness of the proposed method is experimentally demonstrated on two robotic applications, namely the point set registration and the inertial sensor localization.
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Bauchau, Olivier A., and Shilei Han. "Advanced Plate Theory for Multibody Dynamics." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12415.
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In flexible multibody systems, many components are often approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theory, form the basis of the analytical development for plate dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, several high-order and refined plate theory were proposed. While these approaches work well for some cases, they typically lead to inefficient formulation because they introduce numerous additional variables. This paper presents a different approach to the problem, which is based on a finite element discretization of the normal material line, and relies of the Hamiltonian formalism of obtain solutions of the governing equations. Polynomial solutions, also known as central solutions, are obtained that propagate over the entire span of the plate.
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Fasse, Ernest D., and Shilong Zhang. "Lumped-Parameter Modelling of Spatial Compliance Using a Twist-Based Potential Function." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0107.
Full textAbstract:
Abstract This paper examines geometric modelling of elastically coupled, spatial rigid body pairs. For a pair of elastically coupled rigid bodies there exist coincident, unique points on the bodies or their rigid extensions known as centers of stiffness at which translation and rotation are minimally coupled. The rigid body displacement of frames at the centers of stiffness can be associated with a twist displacement, a continuous rigid body motion. A potential function is defined that is a simple quadratic function of the twist displacement. Constitutive equations relating rigid body displacement and wrench are derived. While the problem of modelling and computer simulation is emphasized, the work is also relevant for active compliance control of robotic devices.