Jacobi fields in nonholonomic mechanics

TL;DR

This paper extends the concept of Jacobi fields to nonholonomic mechanics, providing explicit conditions and two formulations for the nonholonomic Jacobi equations based on geometric structures.

Contribution

It introduces a novel definition of Jacobi fields in nonholonomic systems and derives the associated equations using geometric methods.

Findings

Explicit conditions for finding nonholonomic Jacobi fields

Two equivalent formulations of nonholonomic Jacobi equations

Connection to curvature and torsion of nonholonomic connection

Abstract

In this paper, we define Jacobi fields for nonholonomic mechanics using a similar characterization than in Riemannian geometry. We give explicit conditions to find Jacobi fields and finally we find the nonholonomic Jacobi equations in two equivalent ways: the first one, using an appropriate complete lift of the nonholonomic system and, in the second one, using the curvature and torsion of the associated nonholonomic connection.