Vol.2, No 10, 2000 pp. 1035-1048
UDC: 531.314 (045)

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FORMS OF HAMILTON'S PRINCIPLE
FOR NONHOLONOMIC SYSTEMS
Valentin Vitalievich Rumyantsev
Academician, Computing Center of RAS, Russia, Moscow, 117967, ul. Vavilova, 40

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Abstract. The conditions under which the three forms of Hamilon's principle were derived for nonholonomic systems with linear constraints by Hölder, Voronets and Suslov are analysed in the general case of nonlinear constraints. It is proved, that these three forms are equivalent and transformable to each other.
The analogous questions are analysed for the case of nonlinear quasi-coordinates and quasi-velocities. In addition the forms of Hölder, Voronets and Suslov are excibited in the case of Legendre transformation reducing the motion's equations to canonical form in quasi-coordinates. Also the conditions under which Hamilton's principle for nonholonomic systems has the characterictics of the principle of stationary action are derived.

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OBLICI HAMILTONOVOG PRINCIPA
ZA NEHOLONOMNE SISTEME Analiziraju se uslovi pod kojima su izvedena tri oblika Hamiltonovog principa za neholonomne sisteme sa linearnim ograničenjima po Hölder-u, Voronets-u i Suslov-u u opštem slučaju nelinearnih ograničenja. Dokazano je da su ova tri oblika međusobno ekvivalentna i da se mogu transformisati jedan u drugi.
Analizirana su i analogna pitanja za slučaj nelineranih kvazi-koordinata i kvazi brzina. Sem toga oblici Hölder-a, Voronets-a i Suslov-a su prikazani u slučaju Legendre-ove transformacije redukovanjem jednačina kretanja na kanonički oblik u kvazi-koordinatama. Takođe su izvedeni i uslovi pod kojima Hamiltonov princip za za neholonomne sisteme ima karakteristike principa stacionarne akcije.