Abstract
For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange’s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange’s equations show unique advantages over the traditional Lagrange’s equations in symplectic integrations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Feng Kang, Qin Mengzhao. Symplectic Geometric Algorithms for Hamiltonian Systems[M]. Zhejiang Science & Technology Press, Hangzhou, 2003, 271–344.
Edward J Haug. Computer Aided Kinematics and Dynamics of Mechanical Systems[M]. Allyn and Bacon, Needham Heights, Massachusetts, U S, 1989, 305–335.
Shanshin Chen, Daniel A Tortorelli. An energy-conserving and filtering method for stiff nonlinear multibody dynamics[J]. Multibody System Dynamics, 2003, 10(4): 341–362.
Elisabet V Lens, Alberto Cardona, Michel Geradin. Energy preserving time integration for constrained multibody systems[J]. Multibody System Dynamics, 2004, 11(1): 41–61.
Chen S, Tortorelli D A, Hansen J M. Unconditionally energy stable implicit time integration: application to multibody system analysis and design[J]. International Journal for Numerical Methods in Engineering, 2000, 48(6): 791–822.
Simo J C, Tarnow N, Wong K. Exact energy-momentum conserving algorithms and sympectic schemes for nonlinear dynamics[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 100(1): 63–116.
Channell P, Scovel C. Symplectic integration of Hamiltonian systems[J]. Nonlinearity, 1990, 3(2): 231–259.
Leimkuhler B, S. Reich Symplectic integration of constrained Hamiltonian systems[J]. Math Comp, 1994, 63(208): 589–605.
Barth E, Leimkuhler B. Symplectic methods for conservative multibody systems[C]. In: Mardsen J E, Patrick G W, Shadwick W F (eds). Integration Algorithms for Classical Mechanics, Fields Institute Communications. American Mathematical Society, U S, 1996, 25–43.
Leimkuhler B, Skeel R D. Symplectic numerical integrators in constrained Hamiltonian systems[J]. J Comp Phys, 1994, 112(1): 117–125.
Baumgarte J W. A new method of stabilization for holonomic constraints[J]. ASME Journal of Applied Mechanics, 1983, 50(4): 869–870.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, Yj., Ren, Gx. A symplectic algorithm for dynamics of rigid body. Appl Math Mech 27, 51–57 (2006). https://doi.org/10.1007/s10483-006-0107-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0107-z