  The motion of a rigid body is described in Classical Mechanics with the
venerable Euler's equations which are based on the assumption that the relative
distances among the constituent particles are fixed in time. Real bodies,
however, cannot satisfy this property, as a consequence of thermal
fluctuations. We generalize Euler's equations for a free body in order to
describe dissipative and thermal fluctuation effects in a thermodynamically
consistent way. The origin of these effects is internal, i.e. not due to an
external thermal bath. The stochastic differential equations governing the
orientation and central moments of the body are derived from first principles
through the theory of coarse-graining. Within this theory, Euler's equations
emerge as the reversible part of the dynamics. For the irreversible part, we
identify two distinct dissipative mechanisms; one associated with diffusion of
the orientation, whose origin lies in the difference between the spin velocity
and the angular velocity, and one associated with the damping of dilations,
i.e. inelasticity. We show that a deformable body with zero angular momentum
will explore uniformly, through thermal fluctuations, all possible
orientations. When the body spins, the equations describe the evolution towards
the alignment of the body's major principal axis with the angular momentum
vector. In this alignment process, the body increases its temperature. We
demonstrate that the origin of the alignment process is not inelasticity but
rather orientational diffusion. The theory also predicts the equilibrium shape
of a spinning body.
