Variational integrators for hamiltonizable nonholonomic systems
The authors study the design of variational integrators for a certain class of nonholonomic systems. By definition, nonholonomic systems do not possess a variational structure. However, already Chaplygin showed that in certain special cases, suitable time reparametrizations lead to a Hamiltonian form. In this article, the authors consider the Poincaré and the Sundman transformations which have already been much used in the context of symplectic integrators with adaptive step sizes. They design two types of variational integrators for Hamiltonizable Chaplygin systems and apply them to three different examples. The results seem to indicate a superior long-time behaviour compared with standard nonholonomic integrators.
scientific article; zbMATH DE number 6107611