calculating position using follower wheels

[Ether]

Originally Posted by flameout

After lowering the tolerances and calculating bounds for the error (total error should be less than 1e-7), I got the following revised figures...

Spoiler for solution:

Position: (-3.7350, -4.0685)
Distance: 60.8668

That matches my results out to the number of decimal places shown, except I'm getting a 6 instead of a 5 in the fourth decimal place of the Y value.

[flameout]

Originally Posted by Ether

That matches my results out to the number of decimal places shown, except I'm getting a 6 instead of a 5 in the fourth decimal place of the Y value

I re-ran my script once for each of MATLAB's ODE solvers, adjusting the tolerances as necessary to get a reasonable solve time.

Every solver agreed through the fifth decimal place (for the Y value). The stiff solvers needed significantly larger error tolerances and took more steps; their predicted error was much higher.

The nonstiff solvers all agreed through the seventh decimal place.

The lowest predicted error was obtained through the ode113 solver, using a relative tolerance of 100 * epsilon and an absolute tolerance of 10^-12. According to my error estimate, all of the following digits are correct:

Spoiler for solution:

Position: (-3.73497544, -4.06852591)
Distance: 60.86682701

It was interesting going through all the solvers -- many of the stiff solvers had error estimates in excess of 10^-4. I guess this shows that the choice of solver really can have an effect on the error, and not just the solution time.

[Ether]

Originally Posted by flameout

Every solver agreed through the fifth decimal place (for the Y value).

The rotate_CW function has some nasty behavior near zero. So I tried replacing the numerical integration of that function in the region T<0.01 with an analytic solution of a 3rd order Taylor expansion. I'm now matching your results with a time step of 1 microsecond.

Bleary-eyed, time to call it quits for the night.