Spatial rotation driven by random angular velocity (Colored noise)

We consider kinematics of a rigid body rotation about a fixed point. An angular velocity is considered to be a sum of deterministic and random vector-functions. We suppose that the components of the latter are statistically independent small stationary processes. The problem is, for example, important for the theory of a rotational Brownian motion or an error analysis of strapped-down inertial navigation systems. We construct a multiplicative perturbation theory so that the desired matrix is represented as a product of deterministic matrix by random perturbation one. The perturbation matrix is approximately found by the first terms of a matrizant. As example, we consider the constant deterministic velocity and the components of the colored random velocity to be white noises (the Brownian motion), the Ornstein-Uhlenbeck processes, or the time derivative of the Ornwstein-Uhlenbeck processes ("green" noises). In the second case it is shown that a diffusion of an instantaneous rotation angle appears only if the deterministic rotation is not zero.