On a Penalty Function Method for the Simulation of Mechanical Systems Subject to Contraints

摘要

The mathematical properties of a penalty method for the digital simulation of mechanical systems of rigid bodies with constraints are investigated. The solutions of the systems of ordinary differential equations are expanded in Taylor series about a small parameter dependent on the penalty function. Under certain assumptions, the solution is close to that obtained by Lagrange multipliers. A Coulomb friction model is also presented and analyzed. This model has deficiences which are pointed out in two examples.