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Эта публикация цитируется в 36 научных статьях (всего в 36 статьях)
On the Hadamard–Hamel Problem and the Dynamics of Wheeled Vehicles
Alexey V. Borisova, Alexander A. Kilinb, Ivan S. Mamaevc a Moscow Institute of Physics and Technology, Dolgoprudnyi, 141700, Russia
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia
c Steklov Mathematical Institute, ul. Gubkina 8, Moscow, 119991, Russia
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.
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
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd34 https://www.mathnet.ru/rus/rcd/v20/i6/p752
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