Cartesian approach for constrained mechanical systems

TL;DR

This paper develops a Cartesian approach for constrained mechanical systems, describing their motion with first-order differential equations in configuration space, offering a different perspective from traditional Newtonian methods.

Contribution

It introduces a novel Cartesian framework for analyzing constrained mechanical systems with linear velocity constraints, expanding the theoretical tools available.

Findings

Provides a first-order differential equation formulation

Applies Cartesian approach to systems with linear velocity constraints

Offers new insights into the geometry of constrained systems

Abstract

In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential equations in the N dimensional configuration space . In this paper we develop the Cartesian approach for mechanical systems with constraints which are linear with respect to velocity.