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We propose a simple model of human motion as a switching linear dynamical system where the switches correspond to contact forces with the ground. This significantly improves the modeling performance when compared to simpler linear systems, with only marginal increase in complexity. We introduce a novel closed-form (non-iterative) algorithm to estimate the switches and learn the model parameters in between switches. We validate our model qualitatively by running simulations, and quantitatively by computing prediction errors that show significant improvements over previous approaches using linear models.