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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Аннотация:
This paper addresses the problem of an inhomogeneous disk rolling on a horizontal plane. This problem is considered within the framework of a nonholonomic model in which there is no slipping and no spinning at the point of contact (the projection of the angular velocity of the disk onto the normal to the plane is zero). The configuration space of the system of interest contains singular submanifolds which correspond to the fall of the disk and in which the equations of motion have a singularity. Using the theory of normal hyperbolic manifolds, it is proved that the measure of trajectories leading to the fall of the disk is zero.
Ключевые слова:
неголономная механика, регуляризация, устранение особенностей, инвариантная мера, эргодические теоремы, нормальное гиперболическое подмногообразие.
Поступила в редакцию: 03.10.2018 Принята в печать: 05.11.2018
Образец цитирования:
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane”, Regul. Chaotic Dyn., 23:6 (2018), 665–684
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd358 https://www.mathnet.ru/rus/rcd/v23/i6/p665
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