Lie group integration for constrained generalized Hamiltonian system with dissipation by projection method (Q2388243)

For a constrained generalized Hamiltonian system with dissipation, by introducing a Lagrange multiplier and using a projection technique, the Lie group integration method was presented, which can preserve the inherent structure of the dynamic system and the constraint-invariant. First, the constrained generalized Hamiltonian system with dissipative converted to a non-constraint generalized Hamiltonian system, then the Lie group integration algorithm for the non-constraint generalized Hamiltonian system is discussed, finally the projection method for generalized Hamiltonian system with constraint is given. It is found that the constraint invariant is ensured by the projection technique, and after introducing the Lagrange multiplier the Lie group character of the dynamic system cannot be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A numerical example is presented to show the effectiveness of the method.