 Computational Physics
For my project, I decided to test and see if sin(θ) in the equation d2/dt2 θ = -g/L*sin(θ) can be approximated to theta when theta is very small (less than 1). I used Python 3.2.5, NumPy, SciPy, and Matplotlib in order to test and graph a position graph to show if the positions of these two instances are similar as well as demonstrate what happens when the initial angle is very big, which shows that a Simple Pendulum has "chaos." Then I graphed a phase graph to show the stable and unstable points in the pendulum swing and how it is still organized. Then to demonstrate more of "chaos" I solved the Double Pendulum equation and graphed the positions of theta1 and theta2 with different initial values, again showing a perfect example of "chaotic" motion. "Chaos" is when the initial values differ ever so slightly, creating a huge difference in results. Then I graph the Double Pendulum's Phase Space to show that chaotic movement, way less organized than that of a Simple Pendulum. 