## Java Physics Simulation

# Brachistochrone Simulator

Start

January 2018

End

April 2018

## š Results

With a *Īx* of 5 meters and a *Īy* of -3 meters, the following results were derived for the time it takes for the mass to get from *A* to *B*, *t _{AB}*, in seconds: (Note that for the final results, an extremely small

*dt*was used in order to attain a high level of approximation: for this,

*dt*= 1/960,000 sec or 1.04167 Ć 10

^{-6})

Curve | t (sec)_{AB} |
---|---|

`StraightTrack` | 1.5116 |

`CircularTrack` | 1.2679 |

`CycloidArc` | 1.2616 |

Using basic physics calculations, the time it takes for an object to travel from the start of a 5 Ć 3 meter frictionless ramp can be found to be approximately **1.52031 seconds**, making the predictions derived via simulation supposedly within only a **0.57%** error.

## š Write-Up

A LaTeX document detailing the Brachistochrone problem, one of its solutions, and the results of the computational model is available here. It was originally produced to be pasted onto a poster for the UTC Mathematics Poster Competition in 2018.

## š Dependencies

- LWJGL - OpenGL bindings and lightweight game engine for Java
- PNGDecoder - Utility class used for loading
`.png`

images into OpenGL for rendering