 | | 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 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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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 |
| << Previous article | Volume 39, Issue 3 / 2004 | Next article >> |
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