New fractal math tool providing simultaneous reorientation and acceleration of spacecraft

Abstract

Quaternion based math system of spacecraft reorientation is extended by admitting imaginary rotation parameters, thus involving hyperbolic functions. For simplicity only one simple hyperbolic rotation is added as the last one in the series of orthogonal matrices. The scheme is reduced to a single rotation about instant axis, and to transformation of primitive basis on a 2D fractal space of dimension ½. This new tool is proved to simultaneously reorient the spacecraft and to accelerate it the kinematics automatically described as relativistic. With a small speed the problem becomes a classical one.