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Research report: DEIM-RR-07-001

DEIM-RR-07-001 (173.5Kb)
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Cartesian Approach for the Heavy Rigid Body in the Suslov and Veselov Case


Rafael Ramrez and Natalia Sadovskaia



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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 into the study of the three problem: the behavior of the heavy rigid body in the Suslov and Veselov case and the rattleback. The first problem concerns the inertial rotation of a rigid body about a fixed point with a non-holonomic constraints, i.e., the projection of the angular velocity on a certain straight line fixed to the body is equal to zero. The Veselov problem is analogous to the Suslov problem but in this case the projection of the angular velocity is in the fixed exes in the space. The thirst problem consist into the study a convex asymmetric rigid body rolling without sliding on a horizontal plane (rattleback).


Non-holonomic systems, Cartesian approach, Newtonian approach, constraint, differential equation, La