People jumping on trampolines

People Bouncing on Trampolines: Dramatic Energy Transfer, a Table-Top Demonstration, Complex Dynamics and a Zero Sum Game

This webpage supports the following article about people bouncing on trampolines. If you need more information about this article that is not available on this page, please contact Manoj Srinivasan.

Webpage public and last updated on Nov 13, 2013.


Title: People bouncing on trampolines: catastrophic energy transfer, complex dynamics, a table-top experiment, and a zero sum game
Authors: Manoj Srinivasan, Yang Wang, and Alison Sheets
Journal: 8(11): e78645, PLOS ONE, 2013.
Article PDF: PDF and HTML versions are available free at the journal webpage.


Video 1: Dramatic energy transfer between two balls bouncing on a trampoline. A surprisingly simple table-top experiment, which appears to have not been done before We find that dramatic energy transfer can happen between two balls when they bounce on an elastic surface, when both are in simultaneous contact with the elastic surface.


Video 2: Two people bouncing on a trampoline. Thanks to Danny Finn (D.U. Trampoline Club) for kindly providing permission to post this video. This video is of the Dublin Area Seat Drop War Championships. Seat drop war is a game played by two people bouncing on a trampoline, each alternating between bouncing on their 'seat' and jumping on their feet. The goal of the game is to be the last player bouncing. Players lose by either bouncing too high, unable to control their bounce, or by bouncing too low, unable to get back up on their feet.


Video 3: MATLAB simulation of two balls on a trampoline. Produced by program 1 below. Notice that the balls incessantly exchange energy.


Video 4: MATLAB simulation of many balls on a trampoline.This system has aspects that are statistical mechanical. Created by program-2 below.


Software (MATLAB programs)

We provide the key MATLAB programs that help establish the main results in the article. To be practical, we do not provide all the programs that were used for the creation the various figures. But the adventurous reader should be able to modify the programs herein to obtain all our results. If you choose to substantially extend this code, we will probably not be able provide detailed support (but do shoot us a question if you have one).

Program 1. Two balls bouncing vertically on a trampoline. A MATLAB simulation: uses event detection to switch between various phases. Download .zip.

Program 2. MATLAB simulation of many balls bouncing on a trampoline. This simulation does not use event-detection, and solves an ODE with a non-smooth right hand side. The simulation is therefore done with a stiff solver and will be less accurate than the event-detection-based program-1. Download .zip.

Program 3. This program solves the linear programming problem that arises from the game theoretic analysis: trying to find the mixed minimax strategis (or equivalently, mixed Nash) of the zero sum game between the two players. Download .zip.

If you'd like to cite this article, say for using these programs, here is the BibTeX entry for the article for citation:

title = {People bouncing on trampolines: Dramatic energy transfer, a table-top demonstration, complex dynamics and a zero sum game},
author = {M. Srinivasan and A. L. Sheets and Y. Wang},
year = {2013},
volume = {8},
issue = {11},
pages = {e78645},
journal = {PLoS ONE}