Abstract
For the constrained generalized Hamiltonian system with dissipation, by introducing Lagrange multiplier and using projection technique, the Lie group integration method was presented, which can preserve the inherent structure of dynamic system and the constraintinvariant. Firstly, the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system, then Lie group integration algorithm for the non-constraint generalized Hamiltonian system was discussed, finally the projection method for generalized Hamiltonian system with constraint was given. It is found that the constraint invariant is ensured by projection technique, and after introducing Lagrange multiplier the Lie group character of the dynamic system can’t be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A presented numerical example shows the effectiveness of the method.
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Communicated by Zhong Wan-xie
Foundation items: the National Natural Science Foundation of China (10372084); Ho Ying-dong Youth Teacher Foundation (71005); the Doctoral Program Foundation of Education Ministry of China (20010699016); the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment
Biographies: Zhang Su-ying (1967≈), Doctor (E-mail: suyingzhang@yahoo. com. cn); Deng Zi-chen (1964≈), Professor, Doctor Tel: + 86-29-8492157; Fa: +86-29-8495540 E-mail:dweifan@nwpu.edu.cn
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Su-ying, Z., Zi-chen, D. Lie group integration for constrained generalized Hamiltonian system with dissipation by projection method. Appl Math Mech 25, 424–429 (2004). https://doi.org/10.1007/BF02437526
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DOI: https://doi.org/10.1007/BF02437526