# Analysis and experimental study on the Jumping Chain

## TL;DR

This paper investigates the dynamics of a falling chain that jumps, analyzing its stable shape as an inverted catenary, and verifies the theory with experiments, offering insights into complex falling systems.

## Contribution

It provides a detailed theoretical and experimental analysis of the jumping chain, including the shape, parameters, and conditions for jumping, which was not comprehensively studied before.

## Key findings

- The stable suspension shape is an inverted catenary.
- Parameters for the jumping catenary are identified.
- Experimental results verify the theoretical analysis.

## Abstract

A freely falling chain from a cup at certain height can jump. The process can be divided into two parts: a stable suspension and an accelerating procedure. Variational principle and force analysis demonstrate that the shape of stable suspension is an inverted catenary. The requirement of the jumping and the parameters to describe the jumping catenary have been studied in detail, and experiments have been conducted to verify the theoretical analysis. The physical picture of the falling chain could be useful in certain falling systems, providing valuable insight into the dynamical system.