Multibody System Dynamics

, Volume 13, Issue 4, pp 447–463

Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics


DOI: 10.1007/s11044-005-2519-6

Cite this article as:
Glocker, C. & Studer, C. Multibody Syst Dyn (2005) 13: 447. doi:10.1007/s11044-005-2519-6


In this paper, we provide a full instruction on how to formulate and evaluate planar frictional contact problems in the spirit of non-smooth dynamics. By stating the equations of motion as an equality of measures, frictional contact reactions are taken into account by Lagrangian multipliers. Contact kinematics is formulated in terms of gap functions, and normal and tangential relative velocities. Associated frictional contact laws are stated as inclusions, incorporating impact behavior in form of Newtonian kinematic impacts. Based on this inequality formulation, a linear complementarity problem in standard form is presented, combined with Moreau’s time stepping method for numerical integration. This approach has been applied to the woodpecker toy, of which a complete parameter list and numerical results are given in the paper.


unilateral constraints friction impact time stepping linear complementary problem 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.IMES - Center of MechanicsETH ZurichZurichSwitzerland