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The motion of a classical linear rotator hindered by a two-well potential and submitted to random torque-impulses is simulated numerically. Various time autocorrelation functions are extracted, and some corresponding spectral properties are calculated.The previous treatments of the dynamics of the multi-well model for orientational freedom suffer from one or more of the following restrictions : (i) The depth of the well is supposed to be greater than kT; (ii) only the long-time behaviour of the system is considered; (iii) the ratio of the rate of changes of wells to the rate of crossing of the barrier crest is assumed to be a constant close to unity. Without these restrictions, one is faced with the general problem of the statistical dynamics of a hindered rotator in contact with a thermal bath. The aim of this paper is to treat this problem. Since an exact general solution seems a formidable task, a numerical treatment has been used.The nature of the contact with the thermal bath must first be specified. This contact is achieved through fluctuating torques acting on the rotator. We represent these fluctuations by impulses which are random in their strength and their time of occurrence, i.e., by instantaneous impacts from molecules of the medium. It is essential to assume that these impacts produce no discontinuous change in the orientation of the rotator. They only alter its angular velocity in a random manner, as described below.We choose a classical linear rotator along a unit vector u(t), with a moment of inertia I, and we characterize the randomness of the torque impulses as follows.(i) The impulses take place at random times governed by a Poisson law of characteristic time zi (mean time between " collisions ").(ii) The direction of the torque vector is random in the plane perpendicular to the rotator. The component of the angular velocity of the rotator which is parallel to the torque vector is left unchanged by the torque impulse, while its perpendicular component takes a new value w independent of the previous one.* This random value w is governed by a Boltzmann law for one angular degree of freedom ; the distribution function for w is f(w) = JI/2zkT exp -(Iw2/2kT). The components of the angular velocity along the polar and azimuthal directions are thus = w cos c-(& sin 8 cos r -8 , sin 5) sin 5, 1 ; sin 8 = w sin {+(dr sin 8 cos c-8, sin 5) cos c, * These mechanical conditions are equivalent to that of a small hard smooth sphere rigidly bound to the origin, in collision with an identical free sphere : then the torque-impulse is perpendicular to the line of centres of the spheres, and only the velocities along this line are exchanged.