Research report: DEIM-RR-06-003
Title
CARTESIAN APPROACH FOR NONHOLONOMIC SYSTEMS
Author/s
Rafael Ramírez and Natalia Sadovskaia
Date
20-10-2006
Research report type
Recerca
Language
ca
Number of pages
33
Summary
In the history of mechanics, there have been two points of view for studying mechanical systems: The Newtonian and the Cartesian. The Cartesian point of view affirms (by using the modern mathematical language) that it is possible to solve the dynamics problem inside the configuration space. In this paper we develop the Cartesian approach for mechanical systems with constraints which are linear with respect to velocity. The obtained results are illustrated in several examples. In particular, we analyze the behavior of the mechanical system with three degrees of freedom and one non-integrable constraint such as the Chapliguin-Carateodory sleigh, the heavy rigid body in the Suslov case, the
nonholonomically constrained particle in R^3, and the mechanical system with N degrees of freedom and N-1 integrable constraints (we propose a complete solution of the inverse problem in dynamics).
Keywords
Cartesian approach, Newtonian approach, constraint, differential equation, Lagrangian systems, nonho
