INTEGRATION OF THE EQUATIONS OF A ROTATIONAL MOTION OF A RIGID-BODY IN QUATERNION ALGEBRA - THE EULER CASE

A dynamical system is constructed in the multiplicative group of the q uarternion algebra H that serves as the configuration space. A homomor phism H --> SO(3) is used such that the unit sphere S-3 subset of H, i nvariant under the system, is transformed into the rotation group SO(3 ). The homomorphic image of the system is identical with the dynamics of rotational motion of a rigid body. The equations of motion are comp letely integrated in the Euler case. To this end Weierstrass' elliptic functions are used. The following goals are achieved within the frame work 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 (c) in the majority of applications the right-hand sides of the equations of perturbed motion depend polynomia lly on the phase variables, which simplifies the use of computer algeb ra in analytic theories. (C) 1998 Elsevier Science Ltd. All rights res erved.