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Integration of the equations of a rotational motion of a rigid body in quaternion algebra. The Euler case. (English. Russian original) Zbl 1050.70504

J. Appl. Math. Mech. 62, No. 2, 193-200 (1998); translation from Prikl. Mat. Mekh. 62, No. 2, 206-214 (1998).
The author proposes to construct the dynamical system by using a multiplicative group of quaternion algebra in the same way as in the configuration space. Moreover, the homomorphism \(\,H\to SO(3)\,\) is used such that the unit sphere which is invariant with respect to the system is transferred into the group of rotations \(SO(3)\). The results of integration motion equations are presented in the Euler’s case.

MSC:

70E15 Free motion of a rigid body
70-08 Computational methods for problems pertaining to mechanics of particles and systems
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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References:

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