Projection Methods for some Constrained Systems

TL;DR

This paper explores geometric projection methods on manifolds with various structures, motivated by applications in non-holonomic and sub-Riemannian geometry of mechanical systems, providing theoretical tools and illustrative examples.

Contribution

It introduces a pair of projector operators based on almost product structures for constrained systems on manifolds, extending geometric methods in non-holonomic mechanics.

Findings

Development of projection operators for constrained geometric structures

Application to non-holonomic and sub-Riemannian systems

Illustrative examples demonstrating the methods

Abstract

This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric structures (Riemann,resp.Poisson,resp.symplectic).The work is motivated by non-holonomic and sub-Riemannian geometry of mechanical systems on finite dimensional manifolds.Two examples are given.