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The kinematics and dynamics of deterministic physical systems have been afoundation of our understanding of the world since Galileo and Newton. For realsystems, however, uncertainty is largely present via external forces such asfriction or lack of precise knowledge about the initial conditions of thesystem. In this work we focus in the latter case and describe the use ofinference methodologies in solving the statistical properties of classicalsystems subject to uncertain initial conditions. In particular we describe theapplication of the formalism of Maximum Entropy (MaxEnt) inference to theproblem of projectile motion given information about the average horizontalrange over many realizations. By using MaxEnt we can invert the problem and usethe provided information on the average range to reduce the originaluncertainty in the initial conditions, while also achieving additional insightsbased on the shape of the posterior probabilities for the initial conditionsprobabilities and the projectile path distribution itself. The wideapplicability of this procedure, as well as its ease of use, reveals a usefultool by which to revisit a large number of physics problems, from classrooms tofrontier research.

Deterministic physical systems under uncertain initial conditions: the case of maximum entropy applied to projectile motion