Integration of the equations of a rotational motion of a rigid body in quaternion algebra. The Euler case

✍ Scribed by I.I. Kosenko

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 493 KB
• Volume: 62
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(98)00025-2

✦ Synopsis

A dynamical system is constructed in the multiplicative group of the quartemion algebra H that serves as the configuration space. A homomorphism H ~ SO( 3) is used such that the unit sphere S 3 C H, invariant under the system, is transformed into the rotation group SO(3). The homornorphic image of the system is identical with the dynamics of rotational motion of a rigid body. The equations of motion are cc,mpletely integrated in the Euler case. To this end Weierstrass' elliptic functions are used. The following goals are achieved within the framework of the method: (a) when representing the algorithms for modelling the dynamics it suffices to use only one chart from the atlas of the phase space manifold, (b) the point in the configuration space of the actual motion lies on the unit sphere, which ensures the best accuracy in numerical procedures, and (e) in the majority of applications the fight-hand sides of the equations of perturbed motion depend polynomially on the phase variables, which simplifies the use of computer algebra in analytic theories.