Symplectic Methods For Constrained Hamiltonian Systems With Applications Of The Multibody Systems Dynamics

Symplectic methods of the constrained Hamiltonian systems are new numerical methods occurring in recent years. The constrained Hamiltonian systems are relative to the multibody systems, for example, the mechanical systems where dissipative forces can be neglected. The mathematical model of the multibody systems of the constrained or closed loops is of differential- algebraic equations forms. It is a set of differential algebraic equations of index-3, and we call for high index questions. Presently, it is a problem for us to solve the equations. Stiffness question and drift-the errors in the original constraint often occur during the process of solving them. And popular numerical methods have well not solved the questions.This paper base mainly on the idea that the differential algebraic equation is an ordinary differential equation on a manifold, and the simple idea a numerical solution of ordinary is analytic solution of a perturbed differential equation. First we discuss differential manifold. Second, to state the theory of symplectic integrator. Third, we construct model about the constrained Hamiltonian system dynamics, and discuss rulers of algorithm. At last, we are simulating. This paper is organized as follow:1. To review the symplectic methods, and present some topics of research for us;2. To state the mathematical theory of dynamics;3. To construct the theory of symplectic method of equations of the constrained Hamiltonian systems dynamics;4. To construct canonical equation for the constrained Hamiltonian systems dynamics;5. To review the numerical methods of the multibody systems dynamics and applications of the symplectic methods;6. To construct rulers of the alglorithm;7. To illustrate;8. Conclusion.