Time-step adaptivity in variational integrators with application to contact problems

Variable time-step methods, with general step-size control objectives, are developed within the framework of variational integrators. This is accomplished by introducing discrete transformations similar to Poincares time transformation. While gaining from adaptive time-steps, the resulting integrators preserve the structural advantages of variational integrators, i.e., they are symplectic and momentum preserving. As an application, the methods are utilized for dynamic multibody systems governed by contact force laws. A suitable scaling function defining the step-size control objective is derived.