# Circular orbits of a ball on a rotating conical turntable

## TL;DR

This paper investigates the dynamics of a symmetric heavy ball rolling without slipping on a uniformly rotating conical turntable, deriving equations of motion, identifying partial periodic solutions, and analyzing their stability.

## Contribution

It provides a detailed mathematical model and stability analysis of a symmetric ball on a rotating cone, which was not extensively studied before.

## Key findings

- Derived equations of motion for the system
- Identified partial periodic solutions
- Analyzed stability of these solutions

## Abstract

This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are obtained, partial periodic solutions are found and their stability is analyzed.