 | | 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: | | 12895 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8084
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| In English (Mech. Solids): | | 4811 |
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| S. E. Perelyaev, "3D parametrization of the rigid body rotation group in systems of gyroscopic orientation," Mech. Solids. 38 (3), 12-21 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
12-21 |
| Title |
3D parametrization of the rigid body rotation group in systems of gyroscopic orientation |
| Author(s) |
S. E. Perelyaev (Moscow) |
| Abstract |
Basic methods of the introduction of a local (3D) parametrization
of the configuration space of a rigid body with a fixed point (SO(3))
are described and specific features of these methods are characterized.
These methods of 3D parametrization can be utilized for solving a number
of applied problems of dynamics of a rigid body. Apart from the well-known
methods of local parametrization involving three angles
(Eulerian or Euler-Krylov angles),
we consider also the exponential parametrization. Advantages of Cayley's
linear-fractional parametrization as applied to the solution
of the problem of local parametrization of the group SO(3)
are discussed and analyzed. It is shown that Cayley's 3D parametrization
leads to a Riccati-type kinematic equation, which has a nondegenerate
structure. We consider examples of local coordinates based on Rodrigues
and Gibbs vectors and the kinematic equations represented in terms
of these 3D variables. |
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|
| Received |
20 March 2001 |
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