English

Reduction of a Hamilton-Jacobi equation for nonholonomic systems

Mathematical Physics 2019-10-23 v2 Differential Geometry math.MP

Abstract

Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for systems subject to nonholonomic constraints and that are invariant under the action of a group of symmetries. We consider nonholonomic systems subject to linear or nonlinear constraints, with different positioning with respect to the symmetries. We describe the reduction procedure first, to later reconstruct solutions in the unreduced picture, by starting from a reduced Hamilton-Jacobi equation. Examples can be depicted in a wide range of scenarios: from free particles with linear constraints, to vehicle motion.

Keywords

Cite

@article{arxiv.1810.04962,
  title  = {Reduction of a Hamilton-Jacobi equation for nonholonomic systems},
  author = {Oğul Esen and Manuel de León and Víctor Manuel Jiménez Morales and Cristina Sardón},
  journal= {arXiv preprint arXiv:1810.04962},
  year   = {2019}
}