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IssuesArchive of Issues2003-3pp.12-21

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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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