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Crowd motion analysis, where there is interdependence amongst the constituent elements, is a relatively unexplored application area in computer vision. In this work, we propose a fast method for short-term crowd motion prediction using a sparse set of particles. We study the dynamics of a crowd motion model and linear cyclic pursuit. We show that linear cyclic pursuit naturally captures the repulsive and attractive forces acting on the individual crowd member. The pursuit parameters are estimated from videos in an online manner using a feature tracker. Short term trajectory prediction is done by numerical solution of estimated cyclic pursuit equation. We demonstrate the suitability of the proposed technique through extensive experimentations.