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Research report: DEIM-RR-06-003

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DEIM-RR-06-003 (211.2Kb)
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Title

CARTESIAN APPROACH FOR NONHOLONOMIC SYSTEMS

Author/s

Rafael Ramrez 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