Volume 119, Number 6, September 2017
|Number of page(s)||7|
|Published online||14 December 2017|
Chaplygin sleigh with periodically oscillating internal mass
1 Udmurt State University - Universitetskaya 1, Izhevsk, 426034, Russia
2 Kotelnikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch - Zelenaya 38, Saratov, 410019, Russia
3 Steklov Mathematical Institute, Russian Academy of Sciences - ul. Gubkina 8, Moscow, 119991, Russia
Received: 20 October 2017
Accepted: 17 November 2017
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.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 45.40.-f – Dynamics and kinematics of rigid bodies
© EPLA, 2017
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