Java Physics Simulation

Brachistochrone Simulator

Start

January 2018

End

April 2018

Iterative calculus-based simulation with accompanying OpenGL-powered graphics display program designed to verify relative performance of different solutions to the historic Brachistochrone problem. An accompanying report was written in LaTex which gives simulation results and a mathematical explanation of a rigorous solution.
JavaOpenGLLWJGLLaTexGit

simulation

Demonstration of the hill-climbing portion of the simulation, each iteration moving towards the optimal circular arc path as a potential solution to the Brachistochrone Problem.

šŸ Results

With a Ī”x of 5 meters and a Ī”y of -3 meters, the following results were derived for the time it takes for the mass to get from A to B, tAB, 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 Ɨ 10-6)

CurvetAB (sec)
StraightTrack1.5116
CircularTrack1.2679
CycloidArc1.2616

Using basic physics calculations, the time it takes for an object to travel from the start of a 5 Ɨ 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.

šŸ“ƒ 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.

šŸ”— Dependencies

  • LWJGL - OpenGL bindings and lightweight game engine for Java
  • PNGDecoder - Utility class used for loading .png images into OpenGL for rendering