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A general framework for analyzing kinematics of a rigid body is presented. We concentrate on different types of rotational motion of an object, namely the constant rotation, the constant angular acceleration about a fixed axis and the precessional motion. Quaternions are used to formulate the motion analysis problem, assuming the availability of a sequence of position vectors at a uniformly sampled time interval. Computationally efficient recursive algorithms have been developed to estimate the relevant parameters defining the evolution of the attitude of the object. Simulation results indicate good performance of these algorithms even in the presence of high sensor noise. Another advantage of the proposed methods is that they allow a varying number of feature points at different time instants, enabling the algorithms to handle long term occlusion of features in machine vision applications.