Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions

2024/12/04 by Kassotakis, Pavlos, Kouloukas, Theodoros, Nieszporski, Maciej
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2412.03543

Abstract

We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these generic equations. Furthermore, we show that these equations can be reinterpreted as difference systems defined on the \mathbb Z² graph and this reinterpretation relates (unifies) the linear and the non-linear approach of discrete analytic functions.

Related

• On Collisions in Nonholonomic systems
• Dynamic Connections in Analytical Mechanics
• Relativistic and Non-relativistic Equations of Motion
• Nondeterministic particle systems
• Variational Collision Integrators for Nonholonomic Lagrangian Systems