Academic literature on the topic 'Generalised 3-body problem'
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Journal articles on the topic "Generalised 3-body problem"
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Bharti, Aakanksha. "Hazard Exposure and Health Assessment of Construction Workers in New Delhi, India." International Journal of Preventive, Curative & Community Medicine 06, no. 02 (December 21, 2020): 22–27. http://dx.doi.org/10.24321/2454.325x.202009.
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Introduction: Construction workers are at a risk of a number of health-related problems, and are exposed to a plethora of occupational hazards. Due to dearth of studies on construction workers about various determinants playing key role on their health. Objectives: 1) To determine the socio-demographic status of construction workers. 2) To assess workplace hazard exposure among study subjects. 3) To evaluate the overall health of the study subjects. Method: An opportunity was created in a general health camp organised by Department of Community Medicine, VMMC and Safdarjung Hospital, Delhi in collaboration with Central Public Work Department (C.P.W.D) Officers’ Wives Association. All the construction workers attending the health camp were approached and only those who consented were included in the study. An interviewer administered questionnaire was filled for all the study subjects. Along with the questionnaire, detailed clinical examination was done, blood pressure and random blood sugar was measured. Simple tables and cross tables were made to present the data. Result: Total 129 construction workers were included in the study. Nearly 87% of the workers were employed on temporary or contract basis. 63.6% (n=82) spent 8 to 12 hours per day at work. Around half of the construction workers earned Rs. 10,000 per month or less. Thermal stress affected the maximum number of workers (54.3%), followed by dust (53.5%), followed by noise (38%). Around 10% (13) of the workers complained of having some health problem. Various complaints were generalised body ache, headache, weakness, fever, cough, cold, blood in sputum, decreased appetite and blood in stools. Conclusion: Construction workers are suffering from adverse health problems. There is the importance of regulating work hours of construction workers, periodic training on safe work culture and ways to reduce workplace injuries.
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Ershkov, Sergey V. "The Yarkovsky effect in generalized photogravitational 3-body problem." Planetary and Space Science 73, no. 1 (December 2012): 221–23. http://dx.doi.org/10.1016/j.pss.2012.09.002.
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Floría, Luis. "Generalized Gylden-Type Systems in Universal DS-Like TR-Variables." International Astronomical Union Colloquium 172 (1999): 461–62. http://dx.doi.org/10.1017/s0252921100073176.
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Scheifele (1970) applied Delaunay-Similar (DS) elliptic Keplerian elements (with the true anomaly as the independent variable) to the J2 Problem in Artificial Satellite Theory, making an element of the true anomaly. Deprit (1981) views Scheifele’s TR-mapping as an extension of Hill’s transformation from a 6-dimensional phase space to an enlarged, 8-dimensional one. To adapt this approach to elliptic-type two-body problems with a time-varying Keplerian parameter μ(t), Floía (1997, §3, §4) treated a Gylden system (Deprit 1983) and derived “Delaunay-Similar” variables via a TR-like transformation. Now we extend our treatment to perturbed Gylden systems, and modify the TR-map to deal with any kind of two-body orbit. We work out our generalization and the resulting variables within a unified pattern whatever the type of motion, in terms of universal functions (Stiefel & Scheifele 1971, §11; Battin 1987, §4.5, §4.6) and auxiliary angle-like parameters.
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Yarov, Yu Yu, and Yu I. Silenko. "DYNAMICS OF PROAND ANTI-INFLAMMATORY PROSTAGLANDINS IN CASES OF GENERALIZED PERIODONTITIS ACCOMPANIED BY DIFFERENT TYPES OF REACTIVITY OF THE BODY." Ukrainian Dental Almanac, no. 2 (June 27, 2022): 16–21. http://dx.doi.org/10.31718/2409-0255.2.2022.03.
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In terms of socio-economic significance, among the most burning problems of modern dentistry are periodontal diseases. According to modern ideas, in generalized periodontitis, one of the main mechanisms of destruction of the alveolar bone is considered to be an increase in prostaglandin levels. Data on the detection of receptors for PG E2 on the membranes of preosteoblasts and osteoclasts are described. Taking into consideration the effect of prostaglandins F2α and E2 on microvascular and cellular reactions in tissues, we can predict their important role in the development of healing and stabilization of the pathological process in periodontal tissues.
The aim of this research was to study the dynamics of proand anti-inflammatory prostaglandins (F2α and E2) in the blood of patients with generalized periodontitis accompanied by normo-, hyperand hyporeactivity of the body after patch surgery.
Materials and methods of research. 216 people aged 45 between 55 years old with the diagnosis of generalized periodontitis were examined. Depending on the condition of reactivity of the body, the patients were divided into three groups: 11 normoreaction; 2hyperreaction; 3 hyporeaction. After initial therapy, patch surgery was performed according to the indications. Blood sampling was performed after surgery on the 1st, 2nd, 4th, 6th and 9th day. The content of prostaglandins F2α and E2 was determined by radioimmunoassay.
Statistical processing of the obtained digital data was performed using the computer program Statistica 8.0 (STA862D175437Q).
Results of the research. The results of this study showed that for patients with generalized periodontitis accompanied by normoreactivity of the body after surgery by an imbalance between the proand antiinflammatory fractions of eicosanoids is typical. On the 1st day, the value of the PG correlation increased, reaching its maximum level on the 2nd day, exceeding the initial value by 1.8 times (p <0.05). This is due to a sharp increase in the content of PG F2α in the blood of patients with generalized periodontitis accompanied by falling concentrations of PG E2. Subsequently, the alignment of the primary balance of prostaglandins was observed on the 9th day, the correlation of PG F2α / PG E2 reached normal values. The change in the correlation of PG F2α / PG E2 in patients with generalized periodontitis accompanied by hyperreactivity of the body was monophasic in nature with its maximum value on the 1st day after surgery. The value of the correlation increased 1.4 times compared to the original (p <0,05) one. On the 2nd day, there was a significant decrease in the correlation of PG F2α / PG E2 to the value below the initial (0.18 ± 0.04). Subsequently, beginning with the 6th day, in the blood of patients with GP with hyperreactivity of the body, the correlation of eicosanoids was close to the initial one. The change in the correlation of PG F2α / PG E2 in patients with generalized periodontitis accompanied by hyporeactivity of the body was monophasic in nature with its maximum values on the 2-4th day after surgery. The value of the correlation became 1.6 times higher compared to the original (p <0,05) one. Subsequently, beginning with the 6th day, in the blood of patients with GP with hyporeactivity of the body the correlation of eicosanoids close to the original was revealed.
Conclusion. Correction of altered parameters in patients with generalized periodontitis with impaired (hyperand hyporeactivity) of the body with bringing them to values, typical for normoreactivity is considered to be a condition for optimizing the healing of mucosal wounds after surgery and further stabilization of the process in periodontal tissues.
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Chaviaropoulos, P., V. Dedoussis, and K. D. Papailiou. "On the 3-D inverse potential target pressure problem. Part 1. Theoretical aspects and method formulation." Journal of Fluid Mechanics 282 (January 10, 1995): 131–46. http://dx.doi.org/10.1017/s0022112095000061.
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An inverse potential methodology is introduced for the solution of the fully 3-D target pressure problem. The method is based on a potential function/stream function formulation, where the physical space is mapped onto a computational one via a body-fitted coordinate transformation. A potential function and two stream vectors are used as the independent natural coordinates, whilst the velocity magnitude, the aspect ratio and the skew angle of the elementary streamtube cross-section are assumed to be the dependent ones. A novel procedure based on differential geometry and generalized tensor analysis arguments is employed to formulate the method. The governing differential equations are derived by requiring the curvature tensor of the flat 3-D physical Eucledian space, expressed in terms of the curvilinear natural coordinates, to be zero. The resulting equations are discussed and investigated with particular emphasis on the existence and uniqueness of their solution. The general 3-D inverse potential problem, with ‘target pressure’ boundary conditions only, seems to be illposed accepting multiple solutions. This multiplicity is alleviated by considering elementary streamtubes with orthogonal cross-sections. The assumption of orthogonal stream surfaces reduces the number of dependent variables by one, simplifying the governing equations to an elliptic p.d.e. for the velocity magnitude and to a second-order o.d.e. for the streamtube aspect ratio. The solution of these two equations provides the flow field. Geometry is determined independently by integrating Frenet equations along the natural coordinate lines, after the flow field has been calculated. The numerical implementation as well as validation test cases for the proposed inverse methodology are presented in the companion paper (Paper 2).
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Lan, Hsiang-Yun, Ti Yin, Jyu-Lin Chen, Yue-Cune Chang, and Jen-Jiuan Liaw. "Factors Associated With Preterm Infants’ Circadian Sleep/Wake Patterns at the Hospital." Clinical Nursing Research 28, no. 4 (August 9, 2017): 456–72. http://dx.doi.org/10.1177/1054773817724960.
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This prospective repeated-measures study explored potential factors (postmenstrual age, body weight, gender, chronological age, illness severity, and circadian rhythm) related to preterm infants’ circadian sleep/wake patterns. Circadian sleep/wake patterns were measured using an Actiwatch for 3 continuous days in preterm infants (gestational age of 28-36.4 weeks) in a neonatal intensive care unit and hospital nursery. Potential factors associated with circadian sleep/wake patterns were analyzed using the generalized estimating equation. For our sample of 30 preterm infants, better sleep/wake patterns were associated with male gender, younger postmenstrual and chronological age, lower body weight, and less illness severity. Preterm infants’ total sleep time ( B = 41.828, p < .01) and percentage of sleep time ( B = 3.711, p < .01) were significantly longer at night than during the day. These findings can help clinicians recognize preterm infants’ sleep problems, signaling the need to provide individualized support to maintain these infants’ sleep quality during their early life.
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Zhang, Zhidong, and Osamu Suzuki. "A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases." Mathematics 9, no. 22 (November 18, 2021): 2936. http://dx.doi.org/10.3390/math9222936.
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A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.
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Yousuf, Saleem, and Ram Kishor. "Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem." Monthly Notices of the Royal Astronomical Society 488, no. 2 (July 18, 2019): 1894–907. http://dx.doi.org/10.1093/mnras/stz1668.
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ABSTRACT The important aspects of a dynamical system are its stability and the factors that affect its stability. In this paper, we present an analysis of the effects of the albedo and the disc on the zero velocity curves, the existence of equilibrium points and their linear stability in a generalized restricted three-body problem (RTBP). The proposed problem consists of the motion of an infinitesimal mass under the gravitational field of a radiating-oblate primary, an oblate secondary and a disc that is rotating about the common centre of mass of the system. Significant effects of the albedo and the disc are observed on the zero velocity curves, on the positions of equilibrium points and on the stability region. A linear stability analysis of collinear equilibrium points L1, 2, 3 is performed with respect to the mass parameter μ and albedo parameter QA of the secondary, separately. It is found that L1, 2, 3 are unstable in both cases. However, the non-collinear equilibrium points L4, 5 are stable in a finite range of mass ratio μ. After analysing the individual as well as combined effects of the radiation pressure force of the primary, the albedo force of the secondary, the oblateness of both the primary and secondary and the disc, it is found that these perturbations play a significant role in the design of the trajectories in the vicinity of equilibrium points and in the analysis of their stability property. In the future, the results obtained will improve existing results and will help in the analysis of different space missions. These results are limited to the regular symmetric disc and radiation pressure, which can be extended later.
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Nguyen, Thuvan T., Koen A. Mol, and Joseph J. DiStefano. "Thyroid hormone production rates in rat liver and intestine in vivo: a novel graph theory and experimental solution." American Journal of Physiology-Endocrinology and Metabolism 285, no. 1 (July 2003): E171—E181. http://dx.doi.org/10.1152/ajpendo.00239.2002.
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We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces ∼31% and whole intestine ∼6% of whole body T3 from T4. With thyroidal production included, liver contributes ∼15% and intestine ∼3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.
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Smith, Howard. "Fibromyalgia: An Afferent Processing Disorder Leading to a Complex Pain Generalized Syndrome." Pain Physician 3;14, no. 2;3 (March 14, 2011): E217—E245. http://dx.doi.org/10.36076/ppj.2011/14/e217.
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Fibromyalgia is a condition which appears to involve disordered central afferent processing. The major symptoms of fibromyalgia include multifocal pain, fatigue, sleep disturbances, and cognitive or memory problems. Other symptoms may include psychological distress, impaired functioning, and sexual dysfunction. The pathophysiology of fibromyalgia remains uncertain but is believed to be largely central in nature. In 1990 the American College of Rheumatology (ACR) published diagnostic research criteria for fibromyalgia. The criteria included a history of chronic and widespread pain and the presence of 11 or more out of 18 tender points. Pain was considered chronic widespread when all of the following are present: pain in the left side of the body; pain in the right side of the body; pain above the waist; pain below the waist. In addition, axial skeletal pain must be present and the duration of pain must be more than 3 months. A tender point is considered positive when pain can be elicited by pressures of 4 kg/ cm2 or less. For tender points to be considered positive, the patient must perceive the palpation as painful; tenderness to palpation is not sufficient. However, over the next 20 years it became increasingly appreciated that the focus on tender points was not justified. In 2010 a similar group of investigators performed a multicenter study of 829 previously diagnosed fibromyalgia patients and controls using physician physical and interview examinations, including a widespread pain index (WPI), a measure of the number of painful body regions. Random forest and recursive partitioning analyses were used to guide the development of a case definition of fibromyalgia, to develop new preliminary ACR diagnostic criteria, and to construct a symptom severity (SS) scale. The most important diagnostic variables were WPI and categorical scales for cognitive symptoms, un-refreshed sleep, fatigue, and number of somatic symptoms. The categorical scales were summed to create an SS scale. The investigators combined the SS scale and the WPI to recommend a new case definition of fibromyalgia: (WPI ≥ 7 AND SS ≥ 5). Although there is no known cure for fibromyalgia, multidisciplinary team efforts using combined treatment approaches, including patient education, aerobic exercise, cognitive behavioral therapy, and pharmacologic therapies (serotonin norepinephrine reuptake inhibitors [e.g., duloxetine, milnacipran] and alpha 2-delta receptor ligands [e.g., pregabalin]) might improve symptoms as well as function in patients with fibromyalgia. Key Words: Pain, fibromyalgia, fatigue, sleep, duloxetine, pregabalin, milnacipran
Dissertations / Theses on the topic "Generalised 3-body problem"
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JADANZA, RICCARDO DANILO. "Morse index and linear stability of relative equilibria in singular mechanical systems." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2599754.
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We have focussed on the study of the linear stability of some particular periodic orbits (called relative equilibria) in planar singular mechanical systems with SO(2)-symmetry, and we have achieved the results using quite advanced mathematical techniques. These involve some homotopy invariants, such as the spectral flow, and some index theory, namely a theorem stating the equality between the Morse index of an orbit seen as a critical point of a Lagrange action functional and the Maslov index of the fundamental solution of the associated Hamiltonian system. Moreover, what we have found meets one of its most important applications in a generalised n-body problem, that is, an n-body problem with a more general potential.
Book chapters on the topic "Generalised 3-body problem"
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Ting, T. T. C. "Generalization of the Stroh Formalism." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0017.
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It was shown in Chapter 12 that the Stroh formalism can be extended to elastodynamics when the problem is a steady state motion. In this chapter we will see several areas where the Stroh formalism can be generalized. First, the formalism is extended to a group of general boundary conditions that include as special cases the boundary conditions for a traction-free, a rigid, and a slippery surface. Explicit solutions are obtained for the Green's function and the image force in a half-space with a slippery boundary surface subjected to a line dislocation in the half-space. The Stroh formalism is then extended to thermo-anisotropic elasticity where we point out that applications to the interfacial crack may lead to a new and higher order stress singularity. Generalization of the formalism to piezoelectric materials results in an octet formalism for which there are four pairs of complex eigenvalues. Extensions of the Stroh formalism to three-dimensional deformations of anisotropic body require a special attention and are investigated in the next chapter. The Stroh formalism is in terms of the displacement u and the stress function ϕ, both 3-vectors. It is therefore most suitable for boundary conditions that are in terms of the displacement or the surface traction. For a slippery surface the normal component of the displacement and the two tangential components of the surface traction vanish. The boundary conditions are not in terms of u or ϕ, but a mixture of one component from u and two components from ϕ. This destroys the elegant sextic formalism of Stroh. We present here a generalized formalism that is applicable to a class of general boundary conditions. They include as special cases the boundary conditions for a traction-free, a rigid, and a slippery surface. The material presented below is taken from Ting and Wang (1992).
Conference papers on the topic "Generalised 3-body problem"
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van Daalen, Ed. "A Generic Allocation Algorithm for Optimal 6dof Motion Control Including Interaction Effects and Physical Limitations." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-19185.
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Abstract In this paper we consider the allocation problem within the context of optimal motion control for floating or submerged bodies. The purpose of our research is to develop an allocation algorithm which allows for (1) multiple bodies with up to six modes for each body, (2) arbitrary actuator types — azimuthing thrusters, propeller-rudder systems etc., (3) arbitrary objective functions, (4) interaction effects such as forbidden zones, and (5) physical limitations such as saturation. Some ideas presented in [1, 2] were generalised to more widely applicable concepts. Each body has an arbitrary number of actuators, each actuator has an arbitrary number of degrees of freedom. Interaction effects are modelled by means of state-dependent effectivity coefficients. Coupled states, such as propeller thrust and torque, are modelled as linearised constraints. The constrained optimization problem is solved with a combination of Sequential Quadratic Programming and Steepest Descent methods. The Python implementation is coupled with MARIN’s extensible modelling framework (XMF). We demonstrate the generic allocation algorithm for an underwater vehicle with multiple actuator types, physical limitations and coupled states and for a surface vessel with two propeller-rudder systems and a bow tunnel thruster. The results show that the allocation algorithm is able to handle complex configurations with specific physical limitations and coupled modes while adopting a generic approach.
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Murakami, Hidenori, and Takeyuki Ono. "A Variational Derivation of Equations of Motion With Contact Constraints Using SE(3)." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87126.
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For rigid-body systems subjected to non-holonomic constraints, a streamlined method is presented to derive a minimum number of analytical equations of motion. To illustrate the method, a rolling disk problem is considered. In kinematics, an orthonormal coordinate system is attached to the center of mass together with additional coordinate systems introduced to define the connection path. For each coordinate system, a moving frame is defined by explicitly writing the coordinate vector basis and the position vector of the origin, whereby the attitude of the coordinate vector basis and the coordinates of the origin are compactly stored in a 4 × 4 frame connection matrix of the special Euclidean group, SE(3). Contact velocity constraints are transformed to pfaffians to obtain the associated variational constraints. In kinetics, the principle of virtual work is employed. The desired equations of motion are obtained by expressing the translational and angular velocities at the center of mass as the linear functions of the generalized velocities with the coefficients stored in [B]-matrix, and reducing it to [B*]-matrix after incorporating the contact constraints. The method can be easily extended to multi-body systems with both holonomic and non-holonomic constraints.
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Taves, Jay, Alexandra Kissel, and Dan Negrut. "Dwelling on the Connection Between SO(3) and Rotation Matrices in Rigid Multibody Dynamics – Part 1: Description of an Index-3 DAE Solution Approach." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-72057.
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Abstract In rigid multibody dynamics simulation using absolute coordinates, a choice must be made in relation to how to keep track of the attitude of a body in 3D motion. The commonly used choices of Euler angles and Euler parameters each have drawbacks, e.g., singularities, and carrying along extra normalization constraint equations, respectively. This contribution revisits an approach that works directly with the orientation matrix and thus eschews the need for generalized coordinates used at each time step to produce the orientation matrix A. The approach is informed by the fact that rotation matrices belong to the SO(3) Lie matrix group. The numerical solution of the dynamics problem is anchored by an implicit first order integration method that discretizes, without index reduction, the index 3 Differential Algebraic Equations (DAEs) of multibody dynamics. The approach handles closed loops and arbitrary collections of joints. Our main contribution is the outlining of a systematic way for computing the first order variations of both the constraint equations and the reaction forces associated with arbitrary joints. These first order variations in turn anchor a Newton method that is used to solve both the Kinematics and Dynamics problems. The salient observation is that one can express the first order variation of kinematic quantities that enter the kinematic constraint equations, constraint forces, external forces, etc., in terms of Euler infinitesimal rotation vectors. This opens the door to a systematic approach to formulating a Newton method that provides at each iteration an orthonormal rotation matrix A. The Newton step calls for repeatedly solving linear systems of the form Gδ = e, yet evaluating the iteration matrix G and residuals e is inexpensive, to the point where in the Part 2 companion contribution the proposed formulation is shown to be two times faster for Kinematics and Dynamics analysis when compared to the Euler parameter and Euler angle approaches in conjunction with a set of four mechanisms.
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Sljoka, Adnan, Offer Shai, and Walter Whiteley. "Checking Mobility and Decomposition of Linkages via Pebble Game Algorithm." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48340.
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The decomposition of linkages into Assur graphs (Assur groups) was developed by Leonid Assur in 1914 - to decompose a linkage into fundamental minimal components for the analysis and synthesis of the linkages. In the paper, some new results and new methods are introduced for solving problems in mechanisms, bringing in methods from the rigidity theory community. Using these techniques, an investigation of Assur graphs and the decomposition of linkages has reworked and extended the decomposition using the well developed mathematical concepts from theory of rigidity and directed graphs. We recall some vocabulary and provide an efficient algorithm for decomposing 2-dimensional linkages into Assur components using strongly connected decompositions of graphs and a fast combinatorial Pebble Game Algorithm, which has been recently used in the study of rigidity and flexibility of structures and in fast analysis of large biomolecular structures such as proteins. Working on a one degree of freedom mechanism, we apply our algorithm to give the Assur decomposition. The Pebble Game Algorithm on such a mechanism is presented, along with an overview of the key properties and advantages of this elegant algorithm. We show how the pebble game algorithm can be used in the analysis and synthesis of linkages to mechanical engineering community. Core techniques and algorithms easily generalize to 3-dimensional structures, and can be further adapted to entire suite of other (body-bar) types of kinematic structures.