刚体动力学方程的一个辛积分方法

路英杰; 任革学

刚体动力学方程的一个辛积分方法

清华大学工程力学系,北京 100084

详细信息

作者简介:
路英杰(1978- ),男,北京市人,博士(联系人.Tel:+86-10-62772637;E-mail:lu-yj04@mails.tsinghua.edu.cn).

中图分类号: O313.3
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出版历程
- 收稿日期: 2004-05-14
- 修回日期: 2005-09-10
- 刊出日期: 2006-01-15

A Symplectic Algorithm for the Dynamics of a Rigid Body

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China

摘要

摘要: 针对四元数和对应广义动量表示的刚体定点动力学方程，利用一种位移格式的微分—代数方程积分方案，实现了非独立广义动量表示的拉格朗日方程的辛积分算法．数值实验显示该算法具有精度高和保持系统守恒量的特点．更为重要的是，广义动量表示的拉格朗日方程较之传统形式的拉格朗日方程在辛积分中表现出独特的优越性．
- 刚体动力学 /
- 四元数 /
- 广义动量 /
- 辛积分
Abstract: For the dynamics of a rigid body with a fixed point based on 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.
- rigid_body dynamics /
- quaternion /
- generalized momenta /
- symplectic integration

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参考文献(11)

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[3]	CHEN Shan-shin,Daniel A Tortorelli.An energy-conserving and filtering method for stiff nonlinear multibody dynamics[J].Multibody System Dynamics,2003,10(4):341—362. doi: 10.1023/A:1026237902561
[4]	Elisabet V Lens,Alberto Cardona,Michel Geradin.Energy preserving time integration for constrained multibody systems[J].Multibody System Dynamics,2004,11(1):41—61. doi: 10.1023/B:MUBO.0000014901.06757.bb
[5]	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. doi: 10.1002/(SICI)1097-0207(20000630)48:6<791::AID-NME859>3.0.CO;2-Z
[6]	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. doi: 10.1016/0045-7825(92)90115-Z
[7]	Channell P,Scovel C.Symplectic integration of Hamiltonian systems[J].Nonlinearity,1990,3(2):231—259. doi: 10.1088/0951-7715/3/2/001
[8]	Leimkuhler B,S Reich.Symplectic integration of constrained Hamiltonian systems[J].Math Comp,1994,63(208):589—605. doi: 10.1090/S0025-5718-1994-1250772-7
[9]	Barth E,Leimkuhler B.Symplectic methods for conservative multibody systems[A].In:Mardsen J E,Patrick G W,Shadwick W F.Integration Algorithms for Classical Mechanics, Fields Institute Communications[C].U S:American Mathematical Society,1996,25—43.
[10]	Leimkuhler B,Skeel R D.Symplectic numerical integrators in constrained Hamiltonian systems[J].J Comp Phys,1994,112(1):117—125. doi: 10.1006/jcph.1994.1085
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刚体动力学方程的一个辛积分方法

作者简介:
路英杰(1978- ),男,北京市人,博士(联系人.Tel:+86-10-62772637;E-mail:lu-yj04@mails.tsinghua.edu.cn).

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A Symplectic Algorithm for the Dynamics of a Rigid Body

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留言板

刚体动力学方程的一个辛积分方法

作者简介: 路英杰(1978- ),男,北京市人,博士(联系人.Tel:+86-10-62772637;E-mail:lu-yj04@mails.tsinghua.edu.cn).

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出版历程

A Symplectic Algorithm for the Dynamics of a Rigid Body

计量

出版历程

目录

作者简介:
路英杰(1978- ),男,北京市人,博士(联系人.Tel:+86-10-62772637;E-mail:lu-yj04@mails.tsinghua.edu.cn).