Nonlinear nonholonomic constraints

TL;DR

This paper extends Voronec's classical equations from linear to nonlinear nonholonomic systems, comparing different formulations and discussing potential for further generalizations in nonholonomic mechanics.

Contribution

The paper introduces a method to generalize Voronec equations to nonlinear nonholonomic constraints, expanding the theoretical framework of nonholonomic mechanics.

Findings

Extended Voronec equations to nonlinear constraints

Compared formulations of equations of motion

Discussed potential for further extensions

Abstract

One of the founders of the mechanics of nonoholonomic systems is Voronec who published in 1901 a significant generalization of the Caplygin's equations, by removing some restrictive assumptions. In the frame of nonholonomic systems, the Voronec equations are probably less frequent and common with respect to the prevalent methods of quasi--coordinates (Hamel--Boltzmann equations) and of the acceleration energy (Gibbs--Appell equations). In this paper we start from the case of linear nonholonomic constraints, in order to extend the Voronec equations to nonlinear nonholonomic systems. The comparison between two ways of expressing the equations of motion is performed. We finally comment that the adopted procedure is appropriated to implement further extensions.