implicit-known-traj

[Peter230655]

Presently z(x, y) cannot be used.
Just curiosity: would opty/Ipopt need $\frac{dz}{dx}, \frac{dz}{dy}$ only or also the mixed derivative $\frac{d^2z}{dxdy}$?

[moorepants]

If we allow z(x, y) then you will get instances of this in the discrete eoms:

• zi(xi, yi)
• zn(xn, yn)
• zp(xp, yp)

And then you take the partials wrt to xi, yi, xn, yn, xp, yp to form the Jacobian, so only dz/dx and dz/dy will be required in the Jacobian. The Jacobian will never have d^2 partials, those will only appear in the Hessian, which we do not form analytically.

[Peter230655]

Thanks!