Energy balance for nonholonomic nonlinear systems

TL;DR

This paper extends the Voronec equations to nonlinear nonholonomic systems and analyzes the conditions under which mechanical energy is conserved, supported by multiple illustrative examples.

Contribution

It introduces a generalized energy balance framework for nonlinear nonholonomic systems using extended Voronec equations.

Findings

Energy conservation depends on the type of nonlinear constraints.

The extended Voronec equations effectively describe nonlinear nonholonomic systems.

Multiple examples demonstrate the applicability of the theoretical results.

Abstract

We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance of the mechanical energy induced by the equations of motion; the conservation of the energy on the basis of the tipology of the constraint equations is discussed. Several examples are performed.