Аннотация:
In this paper, we develop the results obtained by J.Hadamard and G.Hamel concerning the possibility of substituting nonholonomic constraints into the Lagrangian of the system without changing the form of the equations of motion. We formulate the conditions for correctness of such a substitution for a particular case of nonholonomic systems in the simplest and universal form. These conditions are presented in terms of both generalized velocities and quasi-velocities. We also discuss the derivation and reduction of the equations of motion of an arbitrary wheeled vehicle. In particular, we prove the equivalence (up to additional quadratures) of problems of an arbitrary wheeled vehicle and an analogous vehicle whose wheels have been replaced with skates. As examples, we consider the problems of a one-wheeled vehicle and a wheeled vehicle with two rotating wheel pairs.
Ключевые слова:
nonholonomic constraint, wheeled vehicle, reduction, equations of motion.
The work of A.V.Borisov was carried out within the framework of the state assignment for institutions of higher education. The work of A.A.Kilin was supported by the RFBR grant no. 15-38-20879 mol_a_ved. The work of I.S.Mamaev was supported by the RFBR grant no. 13-01-12462-ofi_m.
Поступила в редакцию: 12.10.2015 Принята в печать: 09.11.2015
Образец цитирования:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles”, Regul. Chaotic Dyn., 20:6 (2015), 752–766
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