Constraint Stabilization of Mechanical Systems in Ordinary Differential Equations Form

Abstract

This work discusses a simple means to add kinematic constraints to existing mechanical problems formulated in terms of ordinary differential equations. The constraints are expressed by algebraic relationships between the co-ordinates of the unconstrained problem. A solution projection approach ensures compliance of the solution with the derivatives of holonomic constraint equations up to second order within the desired accuracy. The structure of the unconstrained problem is not altered, resulting in a simple, little intrusive, yet effective means to enforce kinematic constraints into existing formulations and implementations originally intended to address differential problems, without the complexity of solving differential-algebraic problems or resorting to implicit numerical integration schemes and without altering the number and type of equations of the original unconstrained problem. The proposed formulation is compared with known approaches. Numerical applications of increasing complexity illustrate its distinguishing aspects.