# Quotients of affine connection control systems

## TL;DR

This paper explores conditions under which affine connection control systems can be simplified via quotients that preserve mechanical structures, providing criteria for their existence and analyzing their properties.

## Contribution

It introduces a subclass of quotients for affine connection control systems that maintain mechanical structures, with necessary and sufficient conditions for their existence.

## Key findings

- Identifies conditions for quotient existence that preserve mechanical structures.
- Provides structural analysis of quotient maps and mechanical control systems.
- Establishes both local and global criteria for geodesically accessible systems.

## Abstract

In this paper, we investigate the existence of a subclass of quotients of affine connection control systems, which preserve the mechanical structures. Both local and global sufficient and necessary conditions are given for the geodesically accessible affine connection control systems such that they can admit this subclass of quotients. The structural properties of the quotient map and the quotient mechanical control system are discussed.