Geometrical aspects in the rigid body dynamics with three quadratic controls. (English) Zbl 0986.70009

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 209-224 (2000).
The present paper, a natural continuation of the authors [J. Comput. Math. 17, No. 2, 221-224 (1999; Zbl 0942.65142)], is an excellent survey of rigid body dynamics using geometric methods. After a short introduction which contains some historical aspects, the paper presents the following six sections: The Lie group \(SO(3)\) and its Lie algebra \(so(3)\); The rigid body with three particular controls; Variational formulation of the angular velocity equations; Prequantization; Stability; Numerical integration of the equations \((6.2)\), \((6.3)\).
For the entire collection see [Zbl 0940.00039].


70E99 Dynamics of a rigid body and of multibody systems
70E50 Stability problems in rigid body dynamics
70Q05 Control of mechanical systems
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
53Z05 Applications of differential geometry to physics


Zbl 0942.65142