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Using tools from dynamical systems and systems identification we develop a framework for the study of primitives for human motion, which we refer to as movemes. The objective is understanding human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. In this work we address the problem of defining conditions under which collections of signals are well-posed according to a dynamical model class M and then can generate movemes. Based on the assumption of well-posedness, we develop segmentation and classification algorithms in order to reduce a complex activity into the sequence of movemes that have generated it. Using examples we show that the definition of well-posedness can be applied in practice and show analytically that the proposed algorithms are robust with respect to noise and model uncertainty. We test our ideas on data sampled from five human subjects who were drawing figures using a computer mouse. Our experiments show that we are able to distinguish between movemes and recognize them even when they take place in activities containing more than one moveme at a time.