odes_pendulum

odes_pendulum, considers a variety of topics related to the solution of the pendulum problem and its variations.

The notes:

• odes_pendulum.pdf
• odes_pendulum.tex

Scripts and functions:

• euler.m, accepts values of yprime, n, a, b, y0, and uses Euler's method to approximate the solution from a to b, using n steps, initial condition y0, and the derivative function yprime(t,y).
• pendulum_angle_euler.m, calls euler() to approximate linear and nonlinear pendulum problems for a given initial input angle theta0. Try theta0 = 1, and n = 100, 1000, 1000, and look at how plot and phase plot tell you what's well approximated by the linear model and what's not.
• pendulum_compare_euler.m, calls euler() for approximate result, and compares with exact result.
• pendulum_control_euler.m, uses energy "jolts" to keep a pendulum from running down because of friction.
• pendulum_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• pendulum_exact.m, the exact solution to the pendulum test problem.
• pendulum_friction_euler.m, calls euler() for an approximate solution to the linear pendulum with friction.
• pendulum_friction_prime.m, the right hand side of the equation for the linear pendulum with friction.
• pendulum_nonlinear_euler.m, calls euler() with specific values of n, a, b, y0, and plots the result.
• pendulum_nonlinear_prime.m, the right hand side of the nonlinear pendulum test problem.
• pendulum_ode23.m, calls MATLAB's ode23() with specific values of a, b, y0, and plots the result.
• pendulum_prime.m, the right hand side of the pendulum test problem.
• predator_euler.m, calls euler() with specific values of n, a, b, y0, for the predator problem, and plots the result.
• predator_prime.m, the right hand side of the predator test problem.

Images:

• pendulum_angle_plot.png, compares plots of linear and nonlinear pendulum test problem.
• pendulum_angle_phase.png, compares phase plots of linear and nonlinear pendulum test problem.
• pendulum_compare_plot.png, compares plots of computed and exact solutions of the pendulum test problem.
• pendulum_compare_phase.png, compares phase plots of computed and exact solutions of the pendulum test problem.
• pendulum_control_plot.png, a time plot of an attempt to control the linear pendulum with friction.
• pendulum_control_phase.png, a phase plot of an attempt to control the linear pendulum with friction.
• pendulum_friction_plot.png, a time plot of the linear pendulum with friction.
• pendulum_friction_phase.png, a phase plot of the linear pendulum with friction.
• pendulum_plot.png, a plot of an approximate solution of the pendulum test problem.
• pendulum_nonlinear_plot.png, a plot of an approximate solution of the nonlinear pendulum test problem.
• pendulum_nonlinear_phase.png, a phase plot of an approximate solution of the nonlinear pendulum test problem.
• pendulum_ode23_plot.png, a plot of the solution from ode23() of the pendulum test problem.
• pendulum_ode23_phase.png, a phase plot of the solution from ode23() of the pendulum test problem.
• pendulum_phase.png, a phase plot of an approximate solution of the pendulum test problem.
• predator_plot.png, a plot of an approximate solution of the predator test problem.
• predator_phase.png, a phase plot of an approximate solution of the predator test problem.
• wrecking_ball.png, an image of a wrecking ball.