Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/the-chaplygin-sleigh-with-parametric-excitation-chaotic-dynamics-and-0OVufVuiKw
References (66)
-
E. Vetchanin, A. Kilin (2016)
Free and controlled motion of a body with a moving internal mass through a fluid in the presence of circulation around the bodyDoklady Physics, 61
-
A. Gonchenko, S. Gonchenko, A. Kazakov (2013)
Richness of chaotic dynamics in nonholonomic models of a celtic stoneRegular and Chaotic Dynamics, 18
-
C. Carathéodory (1933)
Der SchlittenZ. Angew. Math. Mech., 13
-
I. Bizyaev (2017)
The inertial motion of a roller racerRegular and Chaotic Dynamics, 22
-
Naomi Leonard (1995)
Periodic forcing, dynamics and control of underactuated spacecraft and underwater vehiclesProceedings of 1995 34th IEEE Conference on Decision and Control, 4
-
J. Ostrowski, A. Lewis, R. Murray, J. Burdick (1994)
Nonholonomic mechanics and locomotion: the snakeboard exampleProceedings of the 1994 IEEE International Conference on Robotics and Automation
-
Développements sur un chapitre de la Mécanique de Poisson -
I. Bizyaev, A. Borisov, I. Mamaev (2014)
The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body insideRegular and Chaotic Dynamics, 19
-
A.V. Borisov, I. S. Mamaev (2017)
An Inhomogeneous Chaplygin SleighRegul. Chaotic Dyn., 22
-
I. Bizyaev, A. Borisov, I. Mamaev (2016)
The Hess—Appelrot system and its nonholonomic analogsProceedings of the Steklov Institute of Mathematics, 294
-
V. Arnold, V. Kozlov, A. Neishtadt (1997)
Mathematical aspects of classical and celestial mechanics (2nd ed.) -
V. Kozlov, S. Ramodanov (2001)
The motion of a variable body in an ideal fluidJournal of Applied Mathematics and Mechanics, 65
-
A. Borisov, A. Kilin, I. Mamaev (2012)
How to control Chaplygin’s sphere using rotorsRegular and Chaotic Dynamics, 17
-
J. M. Osborne, D. V. Zenkov (2005)
Proc. of the 44th IEEE Conf. on Decision and Control (Seville, Spain, Dec) -
J. Sprott (2010)
Elegant Chaos: Algebraically Simple Chaotic Flows -
A. Borisov, A. Kilin, I. Mamaev (2013)
The problem of drift and recurrence for the rolling Chaplygin ballRegular and Chaotic Dynamics, 18
-
A. Lichtenberg, M. Lieberman (1992)
Regular and Chaotic Dynamics -
F. Izrailev, M. Rabinovich, A. Ugodnikov (1981)
Approximate description of three-dimensional dissipative systems with stochastic behaviourPhysics Letters A, 86
-
Valery Kozlov (2016)
Invariant measures of smooth dynamical systems, generalized functions and summation methodsIzvestiya: Mathematics, 80
-
R. Murray, S. Sastry (1993)
Nonholonomic motion planning: steering using sinusoidsIEEE Trans. Autom. Control., 38
-
A. Kilin, E. Vetchanin (2015)
The contol of the motion through an ideal fluid of a rigid body by means of two moving massesNonlinear Dynamics, 11
-
P. Krishnaprasad, D. Tsakiris (2001)
Oscillations, SE(2)-snakes and motion control: A study of the Roller RacerDynamical Systems, 16
-
S.M. Rytov, Y.A. Kravtsov, V. I. Tatarskii (1987)
Principles of Statistical Radiophysics. 1. Elements of Random Process Theory -
S.D. Kelly, M. J. Fairchild, P.M. Hassing, P. Tallapragada (2012)
Proc. of the American Control Conf. (Montreal,QC, Canada, June) -
Cox Pdf (1977)
The Theory Of Stochastic ProcessesThe Mathematical Gazette, 61
-
I. Bizyaev, A. Borisov, I. Mamaev (2016)
Dynamics of the Chaplygin sleigh on a cylinderRegular and Chaotic Dynamics, 21
-
W. Feller (1959)
An Introduction to Probability Theory and Its Applications -
Phanindra Tallapragada, S. Kelly (2017)
Integrability of Velocity Constraints Modeling Vortex Shedding in Ideal FluidsJournal of Computational and Nonlinear Dynamics, 12
-
A. Borisov, A. Jalnine, S. Kuznetsov, I. Sataev, J. Sedova (2012)
Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattlebackRegular and Chaotic Dynamics, 17
-
P. Jung, G. Marchegiani, F. Marchesoni (2016)
Nonholonomic diffusion of a stochastic sled.Physical review. E, 93 1
-
I. Bizyaev, A. Borisov, S. Kuznetsov (2017)
Chaplygin sleigh with periodically oscillating internal massEurophysics Letters, 119
-
J. Osborne, Dimitry Zenkov (2005)
Steering the Chaplygin Sleigh by a Moving MassProceedings of the 44th IEEE Conference on Decision and Control
-
V.V. Kozlov (2016)
InvariantMeasures of Smooth Dynamical SystemsGeneralized Functions and Summation Methods, Russian Acad. Sci. Izv. Math., 80
-
L. Tophøj, H. Aref (2008)
Chaotic scattering of two identical point vortex pairs revisitedPhysics of Fluids, 20
-
Yuri Fedorov, L. García-Naranjo (2010)
The hydrodynamic Chaplygin sleighJournal of Physics A: Mathematical and Theoretical, 43
-
V. Kozlov (2004)
Dynamics of variable systems and lie groupsJournal of Applied Mathematics and Mechanics, 68
-
N. Fufaev (1964)
On the possibility of realizing a nonholonomic constraint by means of viscous friction forcesJournal of Applied Mathematics and Mechanics, 28
-
J. Koiller, R. Markarian, S. Kamphorst, S. Carvalho (1995)
Time-dependent billiardsNonlinearity, 8
-
A. Borisov, A. Kilin, I. Mamaev (2015)
On the Hadamard–Hamel problem and the dynamics of wheeled vehiclesRegular and Chaotic Dynamics, 20
-
A. Borisov, I. Mamaev, I. Bizyaev (2017)
Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanicsRussian Mathematical Surveys, 72
-
E. Ott (2006)
Controlling chaosPhysical review letters, 64 11
-
B. Eckhardt, C. Jung (1986)
Regular and irregular potential scatteringJournal of Physics A, 19
-
N. E. Leonard (1995)
Proc. of the 34th IEEE Conf. on Decision and Control (New Orleans, La., Dec) -
A.A. Kilin, E. V. Vetchanin (2015)
The Control of the Motion through an Ideal Fluid of a Rigid Body by Means of Two Moving MassesNelin. Dinam., 11
-
A. Kilin, E. Pivovarova, T. Ivanova (2015)
Spherical robot of combined type: Dynamics and controlRegular and Chaotic Dynamics, 20
-
S. Kelly, Rodrigo Abrajan-Guerrero (2016)
Planar Motion Control , Coordination , and Dynamic Entrainment for a Singly Actuated Nonholonomic Robot -
T. Pereira, D. Turaev (2014)
Exponential energy growth in adiabatically changing Hamiltonian systems.Physical review. E, Statistical, nonlinear, and soft matter physics, 91 1
-
C. Jung, H. Scholz (1988)
Chaotic scattering off the magnetic dipoleJournal of Physics A, 21
-
A. Borisov, I. Mamaev, I. Bizyaev (2015)
The jacobi integral in nonholonomic mechanicsRegular and Chaotic Dynamics, 20
-
S. Kuznetsov (2015)
Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional modelsRegular and Chaotic Dynamics, 20
-
S. Rytov, Y. Kravtsov, V. Tatarskii, A. Kaplan (1987)
Principles of statistical radiophysics -
F. Lenz, F. Diakonos, P. Schmelcher (2008)
Tunable fermi acceleration in the driven elliptical billiard.Physical review letters, 100 1
-
A.V. Borisov, I. S. Mamaev, I.A. Bizyaev (2017)
Dynamical systems with non-integrable constraints: vaconomic mechanics, sub-Riemannian geometry, and non-holonomic mechanicsUspekhi Mat. Nauk, 72
-
S Bolotin, D Treschev (1999)
Unbounded growth of energy in nonautonomous Hamiltonian systemsNonlinearity, 12
-
(2017)
An Inhomogeneous Chaplygin Sleigh, Regul -
V. Kozlov, D. Onishchenko (2003)
The motion in a perfect fluid of a body containing a moving point massJournal of Applied Mathematics and Mechanics, 67
-
A. Borisov, I. Mamaev (2003)
Strange attractors in rattleback dynamicsPhysics-Uspekhi, 46
-
A. D. Lewis, J.P. Ostrowskiy, J. W. Burdickz, R. M. Murray (1994)
Proc. of the IEEE Internat. Conf. on Robotics and Automation (San Diego, Calif., May) -
A. Borisov, S. Kuznetsov (2016)
Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impactsRegular and Chaotic Dynamics, 21
-
A. Borisov, I. Mamayev (2009)
The dynamics of a Chaplygin sleighJournal of Applied Mathematics and Mechanics, 73
-
S. Chaplygin (2008)
On the theory of motion of nonholonomic systems. The reducing-multiplier theoremRegular and Chaotic Dynamics, 13
-
(2002)
On the Motion of a Body with a Rigid Hull and Changing Geometry of Masses in an Ideal Fluid -
A. Borisov, A. Kazakov, I. Sataev (2014)
The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s topRegular and Chaotic Dynamics, 19
-
S. Kelly, M. Fairchild, Peter Hassing, Phanindra Tallapragada (2012)
Proportional heading control for planar navigation: The Chaplygin beanie and fishlike robotic swimming2012 American Control Conference (ACC)
-
A. Itō (1979)
Successive Subharmonic Bifurcations and Chaos in a Nonlinear Mathieu EquationProgress of Theoretical Physics, 61
-
V. Gelfreich, D. Turaev (2008)
Fermi acceleration in non-autonomous billiardsJournal of Physics A: Mathematical and Theoretical, 41
- Publisher
- Springer Journals
- Copyright
- Copyright © 2017 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354717080056
- Publisher site
- See Article on Publisher Site
Abstract
This paper is concerned with the Chaplygin sleigh with time-varying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction transverse to the plane of the knife edge of the sleigh. In this case, the problem reduces to investigating a reduced system of two first-order equations with periodic coefficients, which is similar to various nonlinear parametric oscillators. Depending on the parameters in the reduced system, one can observe different types of motion, including those accompanied by strange attractors leading to a chaotic (diffusion) trajectory of the sleigh on the plane. The problem of unbounded acceleration (an analog of Fermi acceleration) of the sleigh is examined in detail. It is shown that such an acceleration arises due to the position of the moving point relative to the line of action of the nonholonomic constraint and the center of mass of the platform. Various special cases of existence of tensor invariants are found.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Feb 22, 2018