calculating position using follower wheels

[flameout]

Originally Posted by Ether

How slow was it before? Maxima solves Question 5 in less than half a second:

It took one or two seconds (MATLAB isn't terribly fast). It was entirely numerical, performing a numerical integration (for angle) inside another numerical integration (to get position).

Where it was painfully slow was plotting the position trajectory, where it needed to run the numerical integration inside a numerical integration over and over (plenty of redundant calculations). To get a high-quality plot would have taken over an hour of execution time.

Originally Posted by Ether

Use trapezoidal instead. It's very simple to do and much more accurate, so you can use fewer steps and speed it up even more.

If I really cared about accuracy and speed, I would be using Simpson's Rule integration (perhaps using trapezoidal first to get an error estimate, for adaptive integration). Also, I'd analytically solve for the integrals that are analytically solvable (such as the angle).

Another good technique would be to use an ODE solver rather than pure integration -- if I were to do this, I'd probably use MATLAB's built in 4th/5th order adaptive Runge-Kutta solver (ode45). This would probably be plenty fast as well.

Also see Post 13 for a simple change to improve accuracy so you can use fewer steps and run even faster. Post 15 explains why.

I saw that, and considered doing that. I don't have a good reason for choosing what I did, other than that it "works" and is easy to explain (as a left-hand Riemann sum).

Get yourself a copy of gnuplot. It's free and script-driven, so you can write a script to edit/compile/run/and plot your C++ program.

I really need to learn that sometime...