Swinging Atwood Machine

Overview

This project numerically solves the system of differential equations describing a swinging Atwood machine using the Runge-Kutta method of the 4th order. The program provides a graphical interface where you can set up the parameters and view the resulting trajectory path:

Parameters that can be set in the program menu:

1. Number of steps;
2. Simulation time;
3. Mass ratio of the weights;
4. Initial angle;
5. Initial string length;
6. Initial radial velocity;
7. Initial angular velocity;

Graphs generated by the program:

1. Trajectory of the weight (top left);
2. Relative energy change $\epsilon(t)=|100*\frac{E(t)-E(0)}{E(0)}|$ over time $t$ (top right);
3. Phase portrait #1: dependence of $\dot r(t)$ on $r(t)$ (bottom left);
4. Phase portrait #2: dependence of $\dot \theta (t)$ on $\theta (t)$ (bottom right);

Project Structure

• cpp_qt_project: Contains the C++ code for the Qt project.
• pictures: Contains the trajectory plots generated from the calculations. The filenames follow the format: MassRatio_StartingAngle.png.
• project_overview_RU.pdf: A detailed description of the project in PDF format (in Russian).
• atwood.nb: Additional code written in Wolfram Mathematica. This code solves the problem using the built-in NDSolve method, allowing for result verification and the creation of cool animations like this one:

References

1. B. Tuffilaro, A. Abbot, and J. Griffits. Atwood’s machine. American Journal of Physics, doi: 10.1119/1.13791, 1984. Link
2. Л. Д. Ландау и Е. М Лифшиц. Теоретическая физика: Т.I Механика. Издательство Наука. 1988. --- 216 c.
3. Нефедов Н.Н., Попов В.Ю., Волков В.Т. Обыкновенные дифференциальные уравнения. Курс лекций — М.: Физический факультет МГУ им. М.В. Ломоносова, 2016. — 200 с.