Lie Group Integration for Constrained Generalized Hamiltonian System With Dissipation by Projection Method
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摘要: 针对耗散广义Hamilton约束系统，通过引入拉格朗日乘子和采用投影技术，给出了一种保持动力系统内在结构和约束不变性的李群积分法．首先将带约束条件的耗散Hamilton系统化为无约束广义Hamilton系统, 进而讨论了无约束广义Hamilton系统的李群积分法，最后给出了广义Hamilton约束系统李群积分的投影方法．采用投影技术保证了约束的不变性，引入拉格朗日乘子后，在向约束流形投影时不会破坏原动力系统的李群结构．讨论的内容仅限于完整约束系统, 通过数值例题说明了方法的有效性．
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关键词:
- 耗散广义Hamilton约束系统 /
- 李群积分法 /
- 投影方法
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 constraint-invariant.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 Harrultonian 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 tedtnique,and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be deshroyed while projecting to the constraint manifold The discussion is restricted to the case of bolonomic constraint.A presented numerical example shows the effectiveness of the method. -
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