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Displaying similar documents to “On existence and uniqueness of the solution of the equation of motion for constrained mechanical systems.”

Classification of projective space motions with only plane trajectories

Adolf Karger (1989)

Aplikace matematiky

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The paper contains the solution of the classification problem for all motions in the complex projective space, which have only plane trajectories. It is shown that each such motion is a submanifold of a maximal motion with the same property. Maximal projective space motions with only plane trajectories are determined by special linear submanifolds of dimensions 2, 3, 5, 8 in G L ( 4 , C ) , they are denoted as R , E 1 , . . . , E 6 , S 1 , S 2 and given by explicit expressions.

Solving non-holonomic Lagrangian dynamics in terms of almost product structures.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

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Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

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In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical...