Extended constraint enforcement formulations for finite-DOF systems based on Gauss’s principle of least constraint

This paper aims to contribute to formulations of mathematical models for finite-DOF systems based on the Gauss’s principle of least constraint. A new theorem allows to extend the definition of the Gaussian deviation function, overcoming, without requiring any change of variables, algebraic limitations that arise when this principle is applied to systems for which the generalized mass matrices become singular under relaxation of constraints. As a result of this new theorem, the recursive constraint enforcement algorithm based on Udwadia–Kalaba equation, proposed within the scope of the modular modeling methodology for finite-DOF systems, is generalized. Finally, in a case study based on the classical problem of a knife-edge disc rolling in a plane, three constraint enforcement strategies that combine the application of the theorem herein proposed with conventional numerical integration methods have its results confronted, in two simulation scenarios, with those obtained from a benchmark model of this system.