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

Puta, Mircea; Casu, Ioan

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].

Reviewer: Mircea Crâşmăreanu (Iaşi)

MSC:

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

Keywords:

rigid body dynamics; quadratic control; geometric method; Lie group \(S(3)\); Lie algebra \(so(3)\); variational formulation; angular velocity equation; prequantization; stability; numerical integration

Citations:

Zbl 0942.65142