Chaplygin sleigh with periodically oscillating internal mass

被引：19
|
作者：
Bizyaev, Ivan A. [1 ,3 ]
Borisov, Alexey V. [1 ,3 ]
Kuznetsov, Sergey P. [1 ,2 ]
机构：
[1] Udmurt State Univ, Univ Skaya 1, Izhevsk 426034, Russia
[2] RAS, Kotelnikovs Inst Radio Engn & Elect, Saratov Branch, Zelenaya 38, Saratov 410019, Russia
[3] Russian Acad Sci, Steklov Math Inst, Ul Gubkina 8, Moscow 119991, Russia
来源：
EPL | 2017年 / 119卷 / 06期
基金：
俄罗斯科学基金会;
关键词：
DYNAMICS; RATTLEBACK;
D O I：
10.1209/0295-5075/119/60008
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider the movement of Chaplygin sleigh on a plane that is a solid body with imposed nonholonomic constraint, which excludes the possibility of motions transversal to the constraint element ("knife-edge"), and complement the model with an attached mass, periodically oscillating relatively to the main platform of the sleigh. Numerical simulations indicate the occurrence of either unrestricted acceleration of the sleigh, or motions with bounded velocities and momenta, depending on parameters. We note the presence of phenomena characteristic to nonholonomic systems with complex dynamics; in particular, attractors occur responsible for chaotic motions. In addition, quasiperiodic regimes take place similar to those observed in conservative nonlinear dynamics. Copyright (C) EPLA, 2017
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页数：7
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