Relative Rotations in the Dynamics of Rigid Bodies

Oliver O'Reilly, Department of Mechanical Engineering, University of California at Berkeley

In this talk, we show how results from differential geometry and constrained rod theories may be used to examine relative rotations in the motions of rigid bodies. The resulting expressions for the relative rotations are easily computed. In certain situations, they also provide an attractive alternative to a method developed by Goodman and Robinson in 1958 for calculating the same relative rotation. Related results, using different methods, were recently obtained by Anandan, Hannay, Levi and Montgomery. Partially for the purposes of comparison with their work, we illustrate our results with several classical systems from rigid body dynamics.