LAUSR

In contrast to many systems studied in the field of classical mechanics, models of animal motion are often distinguished in that they are both highly uncertain and evolve in a high-dimensional configuration space Q. Often it is either suspected or known that a particular motion regime evolves on or near some smaller subset $$Q_0\subseteq Q$$ . In some cases, $$Q_0$$ may itself be a submanifold of Q. A general strategy is presented in this paper for constructing empirical-analytical Lagrangian (EAL) models of the mechanics of such systems. It is assumed that the set $$Q_0\,\subseteq \,Q$$ is defined by a collection of unknown holonomic constraints on the full configuration space. Since the analytic form of the holonomic constraints is unknown, EAL models are defined that use experimental observations $$\{z_1,\ldots ,z_N\}\subseteq Q^N$$ to ensure that the approximate system models evolve near the underlying submanifold $$Q_0$$ . This paper gives a precise characterization of a probabilistic measure of the distance from the EAL model to the underlying submanifold.