Efficient dynamic modeling for rigid multi-body systems with contact and impact: An O(n) formulation

摘要

Efficient simulation of dynamical systems becomes more and more important in industry and research. Dynamic modeling of multi-body systems yields highly nonlinear equations of motion. Usually, the accelerations are computed by an explicit inversion of the mass matrix that has the dimension according to the degrees of freedom. This classical foregoing implies high computational effort. In the present contribution, an O(n) formulation is introduced for efficient (recursive) procedure. It is based on the Projection Equation in subsystem representation, structuring the problem into parts and yielding interpretable intermediate solutions. The hereby necessary inversion refers to a reduced mass matrix that has the order of the considered subsystem. Additional constraints like endpoint contact are included via corresponding constraint forces. Avoiding an inversion of the total mass matrix is again successfully applied by a recursive procedure. The impact that occurs in the transition phase between the free system and constrained system is also solved in this sense. Results for the simulation of a plane pendulum motion with changing contact scenarios are presented.