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

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V. Ph. Zhuravlev, "The geometry of conical rotations," Mech. Solids. 39 (3), 5-13 (2004)
Year 2004 Volume 39 Number 3 Pages 5-13
Title The geometry of conical rotations
Author(s) V. Ph. Zhuravlev (Moscow)
Abstract A. Yu. Ishlinskii's solid angle theorem [1] known in the kinematics of orthogonal trihedrals is discussed. A theorem on the translation of the vector along a closed trajectory on the SO(3) group is proved. The latter theorem is conjugate to the former one. Applications in the theory of gyroscopes, physics, and analytical mechanics are considered.
References
1.  A. Yu. Ishlinskii, Mechanics of Special Gyroscopic Systems [in Russian], Izd-vo AN USSR, Kiev, 1952; 2nd edition: Mechanics of Gyroscopic Systems [in Russian], Izd-vo AN SSSR, Moscow, 1963.
2.  W. R. Hamilton, Lectures on Quaternions, Hodges and Smith, Dublin, 1853.
3.  L. E. Goodman and A. R. Robinson, "Effect of finite rotations on gyroscopic sensing device," J. Appl. Mech., Vol. 25, No. 2, pp. 210-213, 1958.
4.  J. H. Hannay, "Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian," J. Phys. A.: Math. Gen., Vol. 18, No. 2, pp. 221-230, 1985.
5.  V. Ph. Zhuravlev, Fundamentals of Theoretical Mechanics [in Russian], Fizmatlit, Moscow, 2001.
6.  Yu. K. Zhbanov and V. Ph. Zhuravlev, "On some properties of finite rotations of a rigid body subjected to a nonholonomic constraint," Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 9-14, 1978.
7.  V. Ph. Zhuravlev, "The solid angle theorem in the dynamics of a rigid body," PMM [Applied Mathematics and Mechanics], Vol. 60, No. 2, pp. 323-326, 1996.
8.  V. N. Branets and I. P. Shmyglevskii, Introduction to the Theory of Strapdown Inertial Navigation Systems [in Russian], Nauka, Moscow, 1992.
9.  A. Yu. Ishlinskii, Applied Problems of Mechanics. Volume 2 [in Russian], Nauka,Moscow, 1986.
10.  G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizadat, Moscow, 1946.
11.  S. M. Rytov, "On the transition from the wave to geometric optics," Doklady AN SSSR, Vol. 18, No. 4-5, pp. 263-266, 1938.
12.  V. V. Vladimirskii, "On the rotation of the polarization plane in a curved light ray," Doklady AN SSSR, Vol. 31, No. 3, pp. 222-225, 1941.
Received 15 January 2004
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