Original manuscript: 2002/08/19
An observer-independent formulation of rigid body dynamics is provided in the general setting of an abstract spacetime. In particular, definitions of (body and spatial) angular and linear velocities and momenta are provided independent of an observer. Rigid motions are defined and their properties are studied in detail. A rigid body is defined in this general setting and its various properties are explored. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime are derived using the conservation of spatial linear and spatial angular momenta. The canonical Galilean group is shown to decompose into rotations, space translations, velocity boosts and time translations and its properties are discussed. The abstract Galilean group is studied in detail and is found to be isomorphic to the canonical Galilean group in the presence of an observer. Various subgroups of the abstract Galilean group are characterized. Total velocities corresponding to a rigid motion are defined. The formulation of rigid body dynamics is then studied in the presence of an observer. It is shown that in this case, the velocities and momenta defined previously project to the well known quantities. Finally, it is seen that the equations of motion derived earlier describe the usual motion given by the solutions of the Euler equations for a rigid body undergoing rigid motion.
Last Updated: Fri Jul 10 07:19:57 2020