Matt's example code for MAE 4780/5780 - Intermediate Dynamics

Various dynamics and MATLAB examples made while TAing for Andy Ruina's intermediate dynamics.

My conventions for files typically are:

• MAIN - usually the file that starts everything
• RHS - a function which can by integrated with ODE45
• derive/deriver - A script which derives equations of motion (usually) auto-writes a MATLAB function.

Lectures 1 & 2

Examples include:

• Euler integration
• Using ODE45
• Event detection in MATLAB's ode solvers (bouncing ball example)
• Symbolic toolbox (solving arm kinematics example)
• Best practices for animation (interpolating in time, change plot object data)

3 Body problem

Three masses attracted by gravity. Includes:

• Derivation script
• Animation and plotting of solutions
• FSOLVE root finding to look for periodic solutions given an initial guess
• A file containing ~15 periodic solutions I found that can be played back.

Handout problem 14

4 masses on a plate, some moving, some not. Find plate motion for 0 angular momentum. Full problem statement is inside the folder. Includes:

• Derivation script
• Animation

Handout problem 19

Weird derivation of simple pendulum with y being horizontal right and x being vertical down. Comes up with a single ODE for y acceleration.

• Mostly about the derivation -- lots of comments in derive.m

OptimVelLaunch

• Projectile launched with quadratic drag.
• Minimize velocity and find launch angle required to hit a target.
• fmincon with a nonlinear constraint.

N Spring-mass

• Derive equations symbolically for n-masses connected by springs with a wall on either side.
• Simulate and animate.