  In this paper the exact analytical solution of the motion of a rigid body
with arbitrary mass distribution is derived in the absence of forces or
torques. The resulting expressions are cast into a form where the dependence of
the motion on initial conditions is explicit and the equations governing the
orientation of the body involve only real numbers. Based on these results, an
efficient method to calculate the location and orientation of the rigid body at
arbitrary times is presented. This implementation can be used to verify the
accuracy of numerical integration schemes for rigid bodies, to serve as a
building block for event-driven discontinuous molecular dynamics simulations of
general rigid bodies, and for constructing symplectic integrators for rigid
body dynamics.
