Nilpotent classical mechanics: s-geometry

TL;DR

This paper introduces a special class of hyperbolic spaces called nilpotent s-geometry, useful for constructing nilpotent systems, demonstrated through a D=2 isotropic harmonic oscillator example.

Contribution

It defines nilpotent s-geometry and explores its properties, providing a new geometric framework for nilpotent classical mechanics.

Findings

Defined nilpotent s-geometry and its properties

Constructed a nilpotent system using a D=2 harmonic oscillator

Illustrated the application of s-geometry in classical mechanics

Abstract

We introduce specific type of hyperbolic spaces. It is not a general linear covariant object, but of use in constructing nilpotent systems. In the present work necessary definitions and relevant properties of configuration and phase spaces are indicated. As a working example we use a D=2 isotropic harmonic oscillator.