Jacobi fields in nonholonomic mechanics

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.

arXiv comment64 pages

References in corpus (4)

• Algebroids - general differential calculi on vector bundles
• On Jacobi fields and canonical connection in sub-Riemannian geometry
• The Jacobiator of nonholonomic systems and the geometry of reduced nonholonomic brackets
• Hamiltonization of solids of revolution through reduction

Cited by in corpus (3)

• Retraction maps: a seed of geometric integrators
• Radial kinetic nonholonomic trajectories are Riemannian geodesics!
• Contact bundle formulation of nonholonomic Maupertuis-Jacobi principle and a length minimizing property of nonholonomic dynamics