Alexandr Karapetyan
119899, Moscow, Vorobyevy gory
Depatment of Mechanics and Mathematics, M.V.Lomonosov Moscow State University
Publications:
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Karapetyan A. V., Kuleshov A. S.
Steady Motions of Nonholonomic Systems
2002, vol. 7, no. 1, pp. 81-117
Abstract
In this review we discuss methods of investigation of steady motions of nonholonomic mechanical systems. General conclusions are illustrated by examples from the rigid bodies dynamics on a absolutely rough horisontal plane.
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Karapetyan A. V.
On Construction of the Effective Potential in Singular Cases
2000, vol. 5, no. 2, pp. 219-224
Abstract
It is known that the problem of an investigation of invariant sets (in particular stationary motions) of mechanical systems with symmetries can be reduced to the problem of the analysis of the effective potential [1-11]. The effective potential represents the minimum of the total mechanical energy with respect to quasivelocities on fixed levels of Noether's integrals corresponding to symmetries of the system. The effective potential is a function in the configuration space depending on constants of Noether's integrals. This function is defined in such points of the configuration space where Noether's integrals independent and can have singularities at some points where these integrals are dependent.
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Karapetyan A. V.
First Integrals, Invariant Sets and Bifurcations in Dissipative Systems
1997, vol. 2, no. 1, pp. 75-80
Abstract
The paper deals with dissipative mechanical systems. Problems of the existance of linear constants of motion and invariant sets, their stability and bifurcation are discussed.
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