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2013
Impact Factor

Sergey Chaplygin

Publications:

Chaplygin S. A.
On Some Generalization of the Area Theorem with Applications to the Problem of Rolling Balls
2012, vol. 17, no. 2, pp.  199-217
Abstract
This publication contributes to the series of RCD translations of Sergey Alexeevich Chaplygin’s scientific heritage. Earlier we published three of his papers on non-holonomic dynamics (vol. 7, no. 2; vol. 13, no. 4) and two papers on hydrodynamics (vol. 12, nos. 1, 2). The present paper deals with mechanical systems that consist of several spheres and discusses generalized conditions for the existence of integrals of motion (linear in velocities) in such systems.
First published in 1897 and awarded by the Gold Medal of Russian Academy of Sciences, this work has not lost its scientific significance and relevance. (In particular, its principal ideas are further developed and extended in the recent article "Two Non-holonomic Integrable Problems, Tracing Back to Chaplygin", published in this issue, see p. 191). Note that non-holonomic models for rolling motion of spherical shells, including the case where the shells contain intricate mechanisms inside, are currently of particular interest in the context of their application in the design of ball-shaped mobile robots.
We hope that this classical work will be estimated at its true worth by the English-speaking world.
Keywords: nonholonomic systems, integration
Citation: Chaplygin S. A.,  On Some Generalization of the Area Theorem with Applications to the Problem of Rolling Balls, Regular and Chaotic Dynamics, 2012, vol. 17, no. 2, pp. 199-217
DOI:10.1134/S1560354712020086
Chaplygin S. A.
On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem
2008, vol. 13, no. 4, pp.  369-376
Abstract
This classical paper by S.A. Chaplygin presents a part of his research in nonholonomic mechanics. In this paper, Chaplygin suggests a general method for integration of the equations of motion for non-holonomic systems, which he himself called the "reducing-multiplier method". The method is illustrated on two concrete problems from non-holonomic mechanics.
This paper produced a considerable effect on the further development of the Russian nonholonomic community. With the help of Chaplygin’s reducing-multiplier theory the equations for quite a number of non-holonomic systems were solved (such systems are known as Chaplygin systems). First published about a hundred years ago, this work has not lost its scientific significance and is hoped to be estimated at its true worth by the English-speaking world.
This publication contributes to the series of RCD translations of Chaplygin’s scientific heritage. In 2002 we published two of his works (both cited in this one) in the special issue dedicated to non-holonomic mechanics (RCD, Vol. 7, no. 2). These translations along with translations of his other two papers on hydrodynamics (RCD, Vol. 12, nos. 1,2) aroused considerable interest and are broadly cited by modern researches.
Keywords: nonholonomic systems, reducing-multiplier theorem, integration
Citation: Chaplygin S. A.,  On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem, Regular and Chaotic Dynamics, 2008, vol. 13, no. 4, pp. 369-376
DOI:10.1134/S1560354708040102
Chaplygin S. A.
One Case of Vortex Motion in Fluid
2007, vol. 12, no. 2, pp.  219-232
Abstract
This text presents an English translation of the significant paper [6] on vortex dynamics published by the outstanding Russian scientist S.A.Chaplygin, which seems to have almost escaped the attention of later investigators in this field. Although it was published more than a century ago, in our opinion it is still interesting and valuable.
Keywords: two-dimensional coherent vortex structures, Lamb-Chaplygin dipole, inviscid fluid
Citation: Chaplygin S. A.,  One Case of Vortex Motion in Fluid, Regular and Chaotic Dynamics, 2007, vol. 12, no. 2, pp. 219-232
DOI:10.1134/S1560354707020074
Chaplygin S. A.
On a Pulsating Cylindrical Vortex
2007, vol. 12, no. 1, pp.  101-116
Abstract
This text presents an English translation of the significant paper [5] on vortex dynamics published by outstanding Russian scientist S.A. Chaplygin (1869-1942), which seem to have escaped the attention of later investigators in this field. Chaplygin's solution includes that of an elliptical patch of uniform vorticity in an exterior field of pure shear. Although it was published more than a century ago, in our opinion it is still interesting and valuable.
Keywords: two-dimentional vortex structures, Chaplygin–Kida elliptical vortex, Kirchhoff elliptical vortex
Citation: Chaplygin S. A.,  On a Pulsating Cylindrical Vortex, Regular and Chaotic Dynamics, 2007, vol. 12, no. 1, pp. 101-116
DOI:10.1134/S1560354707010091
Chaplygin S. A.
On a Ball's Rolling on a Horizontal Plane
2002, vol. 7, no. 2, pp.  131-148
Abstract
Citation: Chaplygin S. A.,  On a Ball's Rolling on a Horizontal Plane, Regular and Chaotic Dynamics, 2002, vol. 7, no. 2, pp. 131-148
DOI:10.1070/RD2002v007n02ABEH000200

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