Dynamical Equation of Post Newtonian Quasi-rigid Body

Abstract

We derive the dynamical equation of a post Newtonian (PN) quasi-rigidbody from the general rotational equation of motion, i.e. the PNrotational equation of motion for a quasi-rigid body. It is emphasizedthat a rotational angular velocity vector and a figure axis besides thefirst post Newtonian (1PN) spin vector can be defined and realized forthe model of a PN quasi-rigid body model constructed recently. Actually,we have shown that the moment of inertia tensor of a quasi-rigid bodycan be transformed into a diagonal form by an orthogonal transformation,which defines the principal axes of inertia of the body. As an example,its torque-free motion is discussed and a PN Poinsot configuration,which is similar to the Newtonian one with a small 1PN correction, issolved.