  This work proposes and investigates a new model of the rotating rigid body
based on the non-twisting frame. Such a frame consists of three mutually
orthogonal unit vectors whose rotation rate around one of the three axis
remains zero at all times and thus, is represented by a nonholonomic
restriction. Then, the corresponding Lagrange-D'Alembert equations are
formulated by employing two descriptions, the first one relying on rotations
and a splitting approach, and the second one relying on constrained directors.
For vanishing external moments, we prove that the new model possesses
conservation laws, i.e., the kinetic energy and two nonholonomic momenta that
substantially differ from the holonomic momenta preserved by the standard rigid
body model. Additionally, we propose a new specialization of a class of
energy-momentum integration schemes that exactly preserves the kinetic energy
and the nonholonomic momenta replicating the continuous counterpart. Finally,
we present numerical results that show the excellent conservation properties as
well as the accuracy for the time-discretized governing equations.
