Variational Integrators for Dissipative Systems With One Degree of Freedom Available to Purchase

Variational integrators are developed for dissipative systems with one degree of freedom. The dissipation considered herein is of simple Rayleigh dissipation type. The present formulation is based not on the Lagrange-d’Alembert principle, but on Hamilton’s principle. A benefit for using variational integration techniques is stressed in this paper. The discrete algorithms are obtained by a stationary condition of action integral, in which the Lagrangian is directly discretized. Unlike the existing algorithms, a coupling term between mass and dissipation exists in the present algorithms. A mixed method, in which a velocity is independent on a position coordinate, is presented for dissipative systems. In order to investigate an accuracy of numerical integrators, we introduce a new parameter in addition to the energy decay. Numerical examples show that the present variational, integrators are available for not only highly but also weakly dissipative systems.