Geodesic
Lagrange's equations in nonholonomic mechanics
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 1, pp. 39-50

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The question on possibility of writing the equations of motion of a nonholonomic system in the form of Lagrange's equations of the 2nd kind for the minimal number of parameters is considered. The corresponding results of J. Hadamard and H. Beghin are discussed. It is proved that in the classic problem on rolling of a rigid body along a fixed plane without sliding the case when all three Chaplygin's equations become Lagrange's equations does not exist. For the same problem with two degrees of freedom the most general kind of nonholonomic constraints that provides the correct using Lagrange's equations without multipliers, is established. Examples are given.
Keywords: constraints, the Lagrange equations of the 1st and 2nd kind, rolling of a rigid body without sliding, possible displacements of a system.
Mots-clés : multipliers of constraints 
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Alexandr S. Sumbatov. Lagrange's equations in nonholonomic mechanics. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/ND_2013_9_1_a3/