https://github.com/jbuckmccready/staticpendulum

https://github.com/jbuckmccready/staticpendulum

Last synced: 26 days ago
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• Host: GitHub
• URL: https://github.com/jbuckmccready/staticpendulum
• Owner: jbuckmccready
• License: mit
• Created: 2014-08-27T03:54:37.000Z (over 10 years ago)
• Default Branch: master
• Last Pushed: 2019-11-06T19:40:58.000Z (about 5 years ago)
• Last Synced: 2024-10-15T13:59:15.744Z (2 months ago)
• Language: C++
• Size: 3 MB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Abstract

A damped electrostatic pendulum is modeled using a system of differential equations and solved using numerical integration methods. A two dimensional map of initial conditions is integrated to construct a colored fractal image formed by the discrete points of convergence. Multiple programmatic solutions were implemented using Mathematica, Python and C++ to compare and improve computational performance. A decrease of two orders of magnitude in computation time was obtained by writing an adaptive step Runge Kutta integration method in C++. With significantly improved computation times high resolution images are constructed and stitched together to form videos that demonstrate how the system progressively changes with varying physical parameters: gravity, air drag, attractor strength, etc. The optimized code enables further statistical analysis, and may be easily modified for other systems of differential equations, initial condition maps, and integration methods.

# Compiling

CMakeLists.txt included. External libraries used: lodepng (https://github.com/lvandeve/lodepng) and jsoncpp (https://github.com/open-source-parsers/jsoncpp). Source for those libraries is included directly in this repository for simplicity but could be better maintained using submodules.

No external libraries are required outside of this repository, but C++11/14 features and libraries are used (greatest performance found using GCC 4.9 using -ffastmath, -O3, etc.). I have only tested on two machines: an AMD Phenom II 720BE with unlocked 4th core and overclocked to 3.3Ghz with Windows 7, and an Intel i7-3630QM Ubuntu laptop. I found GCC to be the fastest, next Clang, and finally MSVC. GCC is very effective at optimizing the tight loops with floating point operations, and I was unable to speed up the integration by writing inline sse intrinsic instructions. However MSVC is significantly slower and may be sped up by writing some sse intrinsic instructions.

# Usage

The program takes in a json map configuration file and png image file name. An example configuration file is provided (map.json).

Example use:

$staticpendulum.exe map.json mapImage.png

# Additional Information

Check the Presentation.pdf for example map images and general overview of the project.