Dynamical Equations

Abstract

Consider a rigid or gyrostatic body. Following the concepts of classical mechanics (for historical remarks, see [1]) we postulate that there exists an inertial frame {O ^I, e^I} such that the mathematical equations based on the laws of Newton and Euler hold, namely:

$${}_I{\bf{\dot P}} = {\bf{F}}$$

((1a))

$${}_I{\bf{\dot H}} = {}_I{\bf{L}}$$

((1b))

Here _I P is the linear momentum of the body with respect to the inertial frame and _I H is the corresponding angular momentum. Dots indicate time derivatives with respect to the inertial frame. Quantities F and _I L are resultants of force and torque on the body, the reference point for the torque being point O ^I. Equations 1 are the basic dynamical equations of motion, founded on independent laws of nature [1]. All subsequent manipulation simply recasts Eqs.1 in alternative forms. Initially we assume that the motions are unconstrained.