Nondeterministic particle systems
Abstract
We consider systems of $ n $ particles that move with constant velocity between collisions. The total momentum of each cluster involved in a collision but not necessarily its kinetic energy is preserved at collisions. As there are no further constraints, these systems are nondeterministic. In particular we examine trajectories with infinitely many collisions. The moment of inertia is a convex function so that the set of collision times is countable and nowhere dense. We prove lower bounds (exponential in the number of so-called chain-closing collisions) for the kinetic energy and the moment of inertia for expanding systems. We also consider the relation of points that can be connected via a nondeterministic trajectory and prove that under some assumptions it is a Lagrangian relation.
Fields of Study & Subjects
Spacecraft Dynamics and Control
Point processes and geometric inequalities
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 51
- Issue
- 0
- Pages
- 193–229
- Publication date
- 1 January 2026