Citation: | Yuan Xinyi, Chen Ju, Tian Qiang. Research on constraints violation in dynamics of multibody systems based on SE(3). Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(8): 2351-2363. DOI: 10.6052/0459-1879-24-022 |
[1] |
Diebel J. Representing attitude: Euler angles, unit quaternions, and rotation vectors. Matrix, 2006, 58(15-16): 1-35
|
[2] |
Udwadia FE, Schutte AD. An alternative derivation of the quaternion equations of motion for rigid-body rotational dynamics. Journal of Applied Mechanics, 2010, 77(4): 044505
|
[3] |
黄子恒. 基于李群的多体系统动力学建模与计算. [硕士论文]. 北京: 北京理工大学, 2021 (Huang Ziheng. Dynamic modeling and computation of multibody systems based on Lie group. [Master Thesis]. Beijing: Beijing Institute of Technology, 2021 (in Chinese)
Huang Ziheng. Dynamic modeling and computation of multibody systems based on Lie group. [Master Thesis]. Beijing: Beijing Institute of Technology, 2021 (in Chinese)
|
[4] |
Munthe-Kaas H. Lie-butcher theory for Runge-Kutta methods. BIT Numerical Mathematics, 1995, 35: 572-587 doi: 10.1007/BF01739828
|
[5] |
Munthe-Kaas H. High order Runge-Kutta methods on manifolds. Applied Numerical Mathematics, 1999, 29(1): 115-127 doi: 10.1016/S0168-9274(98)00030-0
|
[6] |
Zenzerović I. Numerical modelling of dynamics of multibody systems in Lie-group setting. [Master Thesis]. Zagreb: University of Zagreb, 2012
|
[7] |
Chen J, Huang Z, Tian Q. A multisymplectic Lie algebra variational integrator for flexible multibody dynamics on the special Euclidean group SE(3). Mechanism and Machine Theory, 2022, 174: 104918 doi: 10.1016/j.mechmachtheory.2022.104918
|
[8] |
黄子恒, 陈菊, 张志娟等. 多刚体动力学仿真的李群变分积分算法. 动力学与控制学报, 2022, 20(1): 8-17 (Huang Z, Chen J, Zhang Z. Lie group variational integration for multi-rigid body system dynamics simulation. Journal of Dynamics and Control, 2022, 20(1): 8-17 (in Chinese)
Huang Z, Chen J, Zhang Z. Lie group variational integration for multi-rigid body system dynamics simulation. Journal of Dynamics and Control, 2022, 20(1): 8-17 (in Chinese)
|
[9] |
Brüls O, Cardona A, Arnold M. Lie group generalized-α time integration of constrained flexible multibody systems. Mechanism and Machine Theory, 2012, 48: 121-137 doi: 10.1016/j.mechmachtheory.2011.07.017
|
[10] |
Leitz T, de Almagro RTSM, Leyendecker S. Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation-no shear locking. Computer Methods in Applied Mechanics and Engineering, 2021, 374: 113475 doi: 10.1016/j.cma.2020.113475
|
[11] |
Hante S, Tumiotto D, Arnold M. A Lie group variational integration approach to the full discretization of a constrained geometrically exact Cosserat beam model. Multibody System Dynamics, 2022, 54(1): 97-123 doi: 10.1007/s11044-021-09807-8
|
[12] |
顾崴, 刘铖, 安志朋等. 一种基于Hamel形式的无条件稳定动力学积分算法. 力学学报, 2022, 54(9): 2577-2587 (Gu Wei, Liu Cheng, An Zhipeng, et al. An unconditionally stable dynamical integration algorithm based on Hamel’s formalism. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2577-2587 (in Chinese) doi: 10.6052/0459-1879-22-131
Gu Wei, Liu Cheng, An Zhipeng, et al. An unconditionally stable dynamical integration algorithm based on Hamel’s formalism. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2577-2587 (in Chinese) doi: 10.6052/0459-1879-22-131
|
[13] |
Marques F, Souto AP, Flores P. On the constraints violation in forward dynamics of multibody systems. Multibody System Dynamics, 2017, 39: 385-419 doi: 10.1007/s11044-016-9530-y
|
[14] |
Nikravesh PE. Some methods for dynamic analysis of constrained mechanical systems: A survey//Computer Aided Analysis and Optimization of Mechanical System Dynamics. Springer, 1984: 351-368
|
[15] |
Pappalardo CM, Lettieri A, Guida D. Stability analysis of rigid multibody mechanical systems with holonomic and nonholonomic constraints. Archive of Applied Mechanics, 2020, 90: 1961-2005 doi: 10.1007/s00419-020-01706-2
|
[16] |
Wehage KT, Wehage RA, Ravani B. Generalized coordinate partitioning for complex mechanisms based on kinematic substructuring. Mechanism and Machine Theory, 2015, 92: 464-483 doi: 10.1016/j.mechmachtheory.2015.06.006
|
[17] |
Neto MA, Ambrósio J. Stabilization methods for the integration of DAE in the presence of redundant constraints. Multibody System Dynamics, 2003, 10: 81-105 doi: 10.1023/A:1024567523268
|
[18] |
Fisette P, Vaneghem B. Numerical integration of multibody system dynamic equations using the coordinate partitioning method in an implicit Newmark scheme. Computer Methods in Applied Mechanics and Engineering, 1996, 135(1-2): 85-105 doi: 10.1016/0045-7825(95)00926-4
|
[19] |
Baumgarte J. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics and Engineering, 1972, 1(1): 1-16 doi: 10.1016/0045-7825(72)90018-7
|
[20] |
Baumgarte JW. A new method of stabilization for holonomic constraints. ASME Journal of Applied Mechanics, 1983, 50: 869-870 doi: 10.1115/1.3167159
|
[21] |
De Jalón JG, Bayo E. Kinematic and Dynamic Simulation of Multibody Systems: The Real-time Challenge. New York: Springer, 2012
|
[22] |
Bayo E, Ledesma R. Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics. Nonlinear Dynamics, 1996, 9: 113-130 doi: 10.1007/BF01833296
|
[23] |
Braun DJ, Goldfarb M. Eliminating constraint drift in the numerical simulation of constrained dynamical systems. Computer Methods in Applied Mechanics and Engineering, 2009, 198(37-40): 3151-3160 doi: 10.1016/j.cma.2009.05.013
|
[24] |
Gear CW, Leimkuhler B, Gupta GK. Automatic integration of Euler-Lagrange equations with constraints. Journal of Computational and Applied Mathematics, 1985, 12: 77-90
|
[25] |
Kinon PL, Betsch P, Schneider S. The GGL variational principle for constrained mechanical systems. Multibody System Dynamics, 2023, 57(3-4): 211-236 doi: 10.1007/s11044-023-09889-6
|
[26] |
Kinon PL, Betsch P, Schneider S. Structure-preserving integrators based on a new variational principle for constrained mechanical systems. Nonlinear Dynamics, 2023, 111: 14231-14261 doi: 10.1007/s11071-023-08522-7
|
[27] |
Bauchau OA. The finite element method in time for multibody dynamics//International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Boston, 2023
|
[28] |
Manara S, Gabiccini M, Artoni A, et al. On the integration of singularity-free representations of SO(3) for direct optimal control. Nonlinear Dynamics, 2017, 90: 1223-1241 doi: 10.1007/s11071-017-3722-8
|
[29] |
Fotland G, Haugen B. Numerical integration algorithms and constraint formulations for an ALE-ANCF cable element. Mechanism and Machine Theory, 2022, 170: 104659 doi: 10.1016/j.mechmachtheory.2021.104659
|
[30] |
Blajer W. Methods for constraint violation suppression in the numerical simulation of constrained multibody systems—A comparative study. Computer Methods in Applied Mechanics and Engineering, 2011, 200(13-16): 1568-1576 doi: 10.1016/j.cma.2011.01.007
|
[31] |
Müller A, Terze Z. On the choice of configuration space for numerical Lie group integration of constrained rigid body systems. Journal of Computational and Applied Mathematics, 2014, 262: 3-13 doi: 10.1016/j.cam.2013.10.039
|
[32] |
Holm DD. Geometric Mechanics-Part II: Rotating, Translating and Rolling. World Scientific, 2011
|
[33] |
Sonneville V. A geometric local frame approach for flexible multibody systems. [PhD Thesis]. Belgium: Université de Liège, 2015
|
[34] |
Lee T. Computational geometric mechanics and control of rigid bodies. [PhD Thesis]. Michigan: University of Michigan, 2008
|
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