| Contents |
| We focus on the numerical integration of nonsmooth mechanical systems with impacts and friction. Thereby basically, we split non-impulsive and impulsive force propagation. As a consequence, we are able to consistently represent impulsive periods by using the velocity as independent variable and the impact as respective Lagrange multiplier.Further, we can benefit from higher order integration rules in non-impulsive periods using the contact force as Lagrange multiplier and acceleration, velocity or position as independent variable. We bring together these two types of motion in the concept of time-discontinuous Galerkin methods. Thereby, we assume that trial and test functions for the velocity may have jumps across discretization intervals, and that they are of higher order inside discretization intervals.
In this talk, we introduce the idea of this general concept resulting in two families of Runge-Kutta collocation methods and present their theoretical behavior. Then, we focus on half-explicit methods, e.g. containing the explicit trapezoidal rule. We present their numerical behavior within exemplary mechanical systems with impacts and Coulomb friction, e.g. the bouncing ball example or an imperfect slider-crank type mechanism. Thereby, we compare the evaluation of non-impulsive periods on acceleration-force and velocity-force level. |
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