Abstract
For an arbitrary rigid body, all dynamical symmetry points are found, and the directions of the axes of dynamical symmetry are determined for these points. We obtain conditions on the principal central moments of inertia under which the Lagrange and Kovalevskaya cases can be realized for the rigid body. We also analyze the set of orientations of the bases formed by the principal axes of inertia for various points of the rigid body.
Similar content being viewed by others
References
A. G. Kurosh, A Course of Higher Algerba (Nauka, Fizmatlit, Moscow, 1971) [in Russian].
A. I. Lurie, Analytic Mechanics (Fizmatgiz, Moscow, 1961; Springer, Berlin, 2001).
E. J. Routh, Dynamics of a System of Rigid Bodies, Part 1 (Macmillan and Co, London, 1905; Nauka, Fizmatlit, Moscow, 1983).
N. I. Amel’kin, Kinematics and Dynamics of Solids (MFTI, Moscow, 2000) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.I. Amel’kin, 2009, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2009, No. 3, pp. 3–11.
About this article
Cite this article
Amel’kin, N.I. On the dynamical symmetry points and the orientations of the principal axes of inertia of a rigid body. Mech. Solids 44, 333–340 (2009). https://doi.org/10.3103/S0025654409030017
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654409030017