Volume 118, Number 1, April 2017
|Number of page(s)||7|
|Published online||08 June 2017|
Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint
Institute of Mathematics, Information Technologies and Physics, Udmurt State University - Universitetskaya 1, Izhevsk, 426034, Russia and Kotelnikov's Institute of Radio-Engineering and Electronics of RAS, Saratov Branch - Zelenaya 38, Saratov, 410019, Russia
Received: 25 March 2017
Accepted: 19 May 2017
We consider motions of the Chaplygin sleigh on a plane supposing that the nonholonomic constraint is located periodically turn by turn at each of three legs supporting the sleigh. We assume that at switching on the constraint the respective element (“knife-edge”) is directed along the local velocity vector and becomes fixed relatively to the sleigh for a certain time interval till the next switch. Differential equations of the mathematical model are formulated and analytical derivation of a 2D map for the state transformation on the switching period is provided. The dynamics takes place with conservation of the mechanical energy. Numerical simulations show phenomena characteristic to nonholonomic systems with complex dynamics. In particular, on the energy surface attractors may occur responsible for regular sustained motions settling in domains of prevalent area compression by the map. In addition, chaotic and quasi-periodic 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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.