Non-Smooth Spatio-Temporal Coordinates in Nonlinear Dynamics

Abstract

This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of motion to the form, which is convenient for further use of analytical and numerical methods of analyses. Three different types of nonsmooth transformations are discussed as follows: positional coordinate transformation, state variables transformation, and temporal transformations. Illustrating examples are provided.

Symmetry, Geometry and Quantization with Hypercomplex Numbers

“…Notably, the hyperbolic setup allows us to linearise many non-linear problems of classical mechanics. It will be interesting to realise new hyperbolic coordinates introduced to this end in [88][89][90] as a hyperbolic phase space.…”