Solutions of dynamic equations in quaternion model of relativity

Exact and approximate solutions of direct and inverse problems for particle's dynamic equations deduced in the framework of quaternion model of relativity are suggested. Point particles in the approach are regarded as bodies of reference represented by quaternion triads subject to transformations preserving form invariance of quaternion multiplication. Values of forces causing non-inertial motion of frames are estimated from viewpoints of immobile observer and a moving frame. Dynamical characteristics of several types of non-inertial motions (uniformly rectilinearly accelerated frame, relativistic oscillator) are analyzed. A simple variant of relativistic twobody problem is considered in detail, and motion integrals for a particle in a field of central force are found under natural conditions imposed upon the force's potential. A relativistic Kepler-type problem is examined, and deceleration of the space probe Pioneer-10 is estimated. © 2010 American Scientific Publishers.