Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us

IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2016-4pp.415-423

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

<< Previous article | Volume 51, Issue 4 / 2016 | Next article >>
G.M. Rozenblat, "On the Choice of Physically Realizable Parameters when Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies," Mech. Solids. 51 (4), 415-423 (2016)
Year 2016 Volume 51 Number 4 Pages 415-423
DOI 10.3103/S0025654416040051
Title On the Choice of Physically Realizable Parameters when Studying the Dynamics of Spherical and Ellipsoidal Rigid Bodies
Author(s) G.M. Rozenblat (Moscow State Automobile and Road Technical University, Leningradskii pr. 64, Moscow, 125319 Russia,
Abstract The paper presents necessary and sufficient conditions whose must be satisfied by the main geometric and dynamic parameters of spherical, ellipsoidal, or parabolic rigid bodies for their physical realization. The main parameters are both the geometric characteristics of the body boundary (radius of the sphere, semiaxes of the ellipsoid, principal curvatures at the vertex, and the paraboloid center location on its symmetry axis) and the body mass and dynamic characteristics (body mass, displacement of the body center of mass from the center on the paraboloid symmetry axis or from the sphere or ellipsoid center of symmetry, the orientation of the principal central axes of inertia with respect to the principal geometric axes of the shell, and the values of the principal central moments of inertia). The physical realization is understood as the existence of an actual distribution of positive masses inside the sphere, ellipsoid, or paraboloid for which the above-listed characteristics of the body are equal to the chosen ones. Several examples from earlier-published papers dealing with the dynamics of spherical, ellipsoidal, or parabolic bodies with physically unrealizable parameters are given.
Keywords center of mass, principal moments of inertia, spherical rigid body, ellipsoid, paraboloid, physical realization
1.  K. Magnus, Kreisel. Theorie und Anwendungen (Springer, Berlin, 1971; Mir, Moscow, 1974).
2.  C. M. Braams, "On the Influence of Friction on the Motion of a Top," Physica 18 (8-9), 503-514 (1952).
3.  E. J. Routh, Dynamics of Systems of Rigid Bodies (Dover Publ., New York, 1955; Nauka, Moscow, 1983).
4.  A. V. Karapetyan and A. S. Kuleshov, "Steady Motions of Nonholonomic Systems," in Nonholonomic Dynamic Systems. Integrability, Chaos, Strange Attractors, Collected Papers (Inst. Komp'yuter Issled., Moscow-Izhevsk, 2002), pp. 247-295 [in Russian].
5.  A. V. Karapetyan and A. S. Kuleshov, "Methods for Studying Stability and Bifurcation of Steady Motions of Conservative Nonholonomic Systems," in Problems of Mechanics: Collection of Papers Dedicated to A. Yu. Ishlinskii on the Occasion of His 90th Birth Day (Fizmatlit, Moscow, 2003), pp. 429-464 [in Russian].
6.  A. S. Kuleshov, "To the Top Dynamics on a Rough Surface," in Problems of Studying Stability and Stabilization of Motion, Collected Papers (VTs RAN, Moscow, 1999), pp. 130-140 [in Russian].
7.  A. V. Borisov and I. S. Mamaev, "Strange Attractors in Dynamics of Celtic Stones," in Nonholonomic Dynamic Systems. Integrability, Chaos, Strange Attractors, Collected Papers (Inst. Komp'yuter Issled., Moscow-Izhevsk, 2002), pp. 296-320 [in Russian].
8.  R. E. Lindberg and R. W. Longman, "On the Dynamic Behavior of the Wobblestone," Acta Mechanica 49, 81-94 (1983).
9.  M. K. Chochchi, B. Malengie, B. Langerok, and B. Grimonpre, "To Construction of a Prototype of Spherical Chinese Top," Nelin. Din. 8 (2), 391-425 (2012).
10.  I. A. Bizyaev, "Nonintegrability and Obstructions to the Hamiltonianization of a Nonholonomic Chaplygin Top," Dokl. Ross. Akad. Nauk 458 (4), 398-401 (2014) [Dokl. Math. (Engl. Transl.) 90 (2), 631-634 (2014)].
11.  A. V. Borisov, A. O. Kazakov, and I. R. Sataev, "The Reversal and Chaotic Attractor in the Nonholonomic Model of Chaplygin's Top," Regular and Chaotic Dynamics 19 (6), 718-733 (2014).
12.  S. O'Brien and J. L. Synge, "The Instability of the Tippe-Top Explained by Sliding Friction," Proc. Roy. Irish Acad. Sec. A 56 (3), 23-35 (1954).
13.  A. A. Kilin, "The Dynamics of Chaplygin Ball: the Quantitative and Computer Analysis," Regular and Chaotic Dynamics 6 (3), 291-306 (2001).
14.  A. Yu. Moskvin, "Chaplygin Ball with Gyrostat: Singular Solutions,", Nelin. Din. 5 (3), 345-356 (2009).
15.  A. V. Borisov and I. S. Mamaev, "Obstacle to the Reduction of Nonholonomic Systems to the Hamiltonian Form," Dokl. Ross. Akad. Nauk 387 (6), 764-766 (2002) [Dokl. Phys. (Engl. Transl.) 47 (12), 892-894 (2002)].
16.  A. V. Borisov, A. A. Kilin, and I. S. Mamaev, "Property of Being Hamiltonian and Integrability of Suslov Problem," Nelin. Din. 6 (1), 127-142 (2010).
17.  A. Yu. Moskvin, "Rubber Ball on a Plane: Critical Solutions," Nelin. Din. 6 (2), 345-358 (2010).
Received 27 November 2014
Link to Fulltext
<< Previous article | Volume 51, Issue 4 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
Rambler's Top100