Betts 10 50

[Peter230655]

This may be a candidate for examples-gallery for these reasons:

• Let $t_0, t_f$ be the starting and the final times of the simulation. There are instance constraints $x_i(t_0) = x_j(t_f)$ which to my knowledge opty cannot handle at the moment. So I iterate over the problem and reset the instance constraints at each iteration. At least in this example (and another one I did) this converged to fulfill these instance constraints.
• there are inequalities in the equations of motion. So, I define additional state variables to handle this. This is not new in the sense that I did this in PR # 269

The minimum given in Betts' book is missed by over 12%. So, I guess this "iteration - solution" is only a 'crutch' until opty can handle this type of situation.

[Peter230655]

Instance constrains like $x_2(t_f) - x_1(t_0)$ are possible with opty, so I changed the simulation accordingly.
I do not believe there is such an example it examples-gallery, yet.