Derivation of theories: structures of the derived system in terms of those of the original system in classical mechanics

TL;DR

This paper introduces a technique to derive higher-degree-of-freedom theories from existing systems in classical mechanics, enabling the construction of more complex integrable systems based on simpler ones.

Contribution

The paper presents a method to systematically derive theories with increased degrees of freedom from original systems, allowing calculation of all quantities of the new system from the original.

Findings

Technique for deriving $(n+1)f$-degree theories from $f$-degree theories

Method to construct new integrable systems with more degrees of freedom

All quantities of the derived system can be computed from the original system

Abstract

We present the technique of derivation of a theory to obtain an $(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and show that one can calculate all of the quantities of the derived theory from those of the original one. Specifically, we show that one can use this technique to construct, from an integrable system, other integrable systems with more degrees of freedom.