  In the first of two papers, we study the initial boundary-value problem that
underlies the theory of the Boltzmann equation for general non-spherical hard
particles. In this work, for two congruent ellipses and for a large class of
associated boundary conditions, we identify initial conditions for which there
do not exist local-in-time weak solutions of Newton's equations of motion. To
our knowledge, this is the first time the necessity of rolling in the
energy-conserving dynamics of strictly-convex rigid bodies has been
demonstrated. This study was, in part, motivated by a recent observation of
Palffy-Muhoray, Virga, Wilkinson and Zheng on the interpenetration of
strictly-convex rigid bodies.
