An improved energy and constraint conserving algorithm for constrained hamiltonian systems

In this paper, an improved Verlet's method, has been proposed to solve the differential-algebraic equations (DAEs). Firstly, a parameter is introduced to modify the Verlet's method to preserve energy exactly. Then, a new algorithm scheme is developed to discretize DAEs in the constrained Hamiltonian systems. The constraint equations are accurately satisfied at each time step, and the problem of constraint violation is avoided. Finally, numerical results confirm the validity of present method by comparing the results with those reported in the published literature. It is also found that the proposed algorithm is suitable for both the weak and strong nonlinear constrained Hamiltonian systems with the properties of high accuracy, long-term stability, and the proposed method is potentially useful for the application of trajectory of tethered satellites.