Adding kinematic constraints to purely differential dynamics

摘要

The dynamics of unconstrained mechanical systems is governed by Ordinary Differential Equations (ODEs). When kinematic constraints need to be accounted for, Differential-Algebraic Equations (DAEs) arise. This work describes the introduction of kinematic constraints, expressed as algebraic relationships between the coordinates of unconstrained mechanical systems, ensuring compliance of the solution with up to the second-order derivative of holonomic constraint equations within the desired accuracy, without altering the ODE structure of the unconstrained problem. This represents a simple, little-intrusive, yet effective means to enforce kinematic constraints into existing formulations and implementations originally intended to address ODE problems, without the complexity of solving DAEs 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 to known approaches. Numerical applications of increasing complexity illustrate its distinguishing aspects.