Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions

Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S.

doi:10.1007/s11071-019-05325-7

Nonlinear Dyn

2019

DOI: 10.1007/s11071-019-05325-7

|View full text |Cite

Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions

Ivan A. Bizyaev

Alexey V. Borisov

Ivan S. Mamaev

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hierarchy of types of behavior of nonholonomic systems includes a variety of cases ranging from simple (integrable) to complex (nonintegrable) ones, the features are associated with a number of inherent invariants and symmetries [9][10][11]. A typical example is the motion of a solid body with a convex smooth surface on a rough plane (the rattleback, or the Celtic stone [12]).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint

Кузнецов¹

2017

EPL

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

“…To reduce the description one can use the fact that the first three eqs. (10) form a separate set independent of the last two equations, and allow analytical integration. Since the energy W given by ( 12) remains constant, we seek the solution in the form…”

mentioning

confidence: 99%

Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint

Кузнецов¹

2017

EPL

View full text Add to dashboard Cite

show abstract

Parametric roll oscillations of a hydrodynamic Chaplygin sleigh

Loya,

Tallapragada

2023

Nonlinear Dyn

View full text Add to dashboard Cite

A Simple Physical Model for Control of a Propellerless Aquatic Robot

Karavaev

Klekovkin

Mamaev

et al. 2021

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

This paper is concerned with the motion of an aquatic robot whose body has the form of a sharp-edged foil. The robot is propelled by rotating the internal rotor without shell deformation. The motion of the robot is described by a finitedimensional mathematical model derived from physical considerations. This model takes into account the effect of added masses and viscous friction. The parameters of the model are calculated from comparison of experimental data and numerical solution to the equations of rigid body motion and the Navier – Stokes equations. The proposed mathematical model is used to define controls implementing straight-line motion, motion in a circle and motion along a complex trajectory. Experiments for estimation of the efficiency of the model have been conducted.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions

Cited by 5 publications

References 23 publications

Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint

Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint

Parametric roll oscillations of a hydrodynamic Chaplygin sleigh

A Simple Physical Model for Control of a Propellerless Aquatic Robot

Contact Info

Product

Resources

About