Lie Group Integration Method for Dissipative Generalized Hamiltonian System with Constraints

A dissipative generalized Hamiltonian system with constraints can be viewed as a generalized Hamiltonian system on a manifold, but its numerical computations must be performed on Rⁿ. In this paper, an effective method is given for constructing the ordinary differential equation system in Euclidean space, in which the constraint manifold is embedded. The above method can preserve the constraint manifold as an invariant one. Then, a generalized Hamiltonian system with constraints is reduced to an unconstrained ordinary differential equation system. Finally, the stability of the constraint-invariant along solution curve is investigated numerically and analytically.