The rigid rotator is chosen as model for the description of a finite many-particle system, leading to the rotation group \(\mathrm{SO}(3,\mathbb{R})\) as configuration space, while the dynamics is a Hamiltonian flow on \(M=T^* \mathrm{SO}(3,\mathbb{R})\). The Euler parametrization for the rotation group is used, and a description of the invariant vector fields is presented. A classical Hamiltonian is associated with the rigid rotator on the symplectic manifold \((M,\Omega)\). To the elementary rotator \(\mu\) it is associated a classical phase-space \((M_{\mu},\Omega_{\mu})\) and it is constructed the phase-space \((M_{\Gamma},\Omega_{\Gamma})\) consisting of \(N\) identical rotators. A statistical description of the ensemble is considered by a partition of each manifold \(M_{\mu}\) in infinitesimal cells.The distribution function \(F\) of the probability distribution evolves according to Liouville continuity equation on \(M\). The author is looking for a solution \(\Theta|_{\Lambda}=d S\), where \(\Omega =- d\Theta\) and \(\Lambda \) is a Lagrangian submanifold of \(M\), while \(S\) is the generating function of the Hamilton-Jacobi theory. Passing to the Fourier transform of the particular solution, it is obtained the so called coherent solution \(f\), the denomination coming from the fact the time evolution keeps the same aspect. By a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum, the solution becomes a Wigner-type quasiprobability distribution. The results are compatible with the standard quantization of the anisotropic rotator, with a shift in the expected value of the Hamiltonian. It is shown that when the quasiprobability distribution follows the Liouville equation, the corresponding wave function verifies the time-dependent Schrödinger equation.