Explicit energy conserving method of two classical dynamical systems

Two classical dynamical systems, the pendulum problem and the Hénon Heiles system, are transformed into the reformulated systems by the nonlinear transformation. These new reformulated systems are transformed into ordinary differential equations on manifolds by the linear transformation. The explicit RKMK method, which is a kind of Lie group method, is applied to solve the differential equations on manifolds. The explicit energy conserving schemes of the two classical dynamical systems are obtained. Numerical simulation investigates the effectiveness of these new schemes in preserving the conservation property of these equations and well simulating dynamical behaviors.