Rigid body mechanics in Galilean spacetimes

Abstract

An observer-independent formulation of rigid body dynamics is provided in the general setting of a Galilean spacetime. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime are derived on the basis of the principle of conservation of spatial momentum. The formulation of rigid body dynamics is then studied in the presence of an observer. It is seen that an observer defines a connection such that there exist rigid motions that are horizontal with respect to this connection that give the same physical motion of the rigid body, and for which the general equations of motion are exactly the usual Euler equations for a rigid body undergoing rigid motion.