The goal of this project is to apply my knowledge of Lagrangian and Hamiltonian formalisms (Physics 311) as well as applied dynamical systems (Math 415/519) to predict when the second pendulum will 'flip'. Unlike the simple pendulum one might analyze in an introductory physics class, the double pendulum is chaotic; hence, I have employed numerical methods to solve the equations of motion which is then validated by my analytical derivations. The final result is a beautiful fractal.
In my full analysis (linked below), I have provided a general project description, mathematical/physical model, and a numerical analysis that is complete with my MATLAB source code.
Analysis:
tjjones6.githu...
Inspiration Paper:
www.famaf.unc....
My Academic Portfolio:
tylerjoneswork...
Негізгі бет The Double Pendulum Fractal
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