We will be concerned with three topics: reduction of the order of the equations of motion, kinematic interpretation of the motion, and existence of invariant relations of equations of motion.
Our starting point is a system of six equations, the so-called EULER and POISSON equations of motion of a heavy rigid body about a fixed point. The three known first integrals of this system permit us, at least in principle, to reduce the order of this system to three, or, if we eliminate the independent variable, even to two. There have been several attempts actually to carry out such a reduction of the order but in several cases the reduction remained hlfway, resulting for example in a system of order four, or being carried out subject to certain conditions on the parameters of the system.