  Intrinsic thermal fluctuations within a real solid challenge the rigid body
assumption that is central to Euler's equations for the motion of a free body.
Recently, we have introduced a dissipative and stochastic version of Euler's
equations in a thermodynamically consistent way (European Journal of Mechanics
- A/Solids 103, 105184 (2024)). This framework describes the evolution of both
orientation and shape of a free body, incorporating internal thermal
fluctuations and their concomitant dissipative mechanisms. In the present work,
we demonstrate that, in the absence of angular momentum, the theory predicts
that principal axis unit vectors of a body undergo an anisotropic Brownian
motion on the unit sphere, with the anisotropy arising from the body's varying
moments of inertia. The resulting equilibrium time correlation function of the
principal eigenvectors decays exponentially. This theoretical prediction is
confirmed in molecular dynamics simulations of small bodies. The comparison of
theory and equilibrium MD simulations allow us to measure the orientational
diffusion tensor. We then use this information in the Stochastic Dissipative
Euler's Equations, to describe a non-equilibrium situation of a body spinning
around the unstable intermediate axis. The agreement between theory and
simulations is excellent, offering a validation of the theoretical framework.
