Method of Calculating Periodic Solutions of Second Order Dynamical Systems

摘要

In this work several numerical procedures for finding periodic solutions of Hamiltonian systems with Hamiltonian H(p,q) = sq p + V(q) are considered. The original system of equations is replaced by a constrained variational problem. Numerical procedures are constructed by using the method of transformation of the objective functional applied to this variational problem. Global convergence results are established and different aspects of numerical implementation of the method are discussed.