Find the optimal angle for which the nonlinear trajectory reaches a given target. While an elementary physics problem at heart, the solution nicely illustrates the evolution from a simple simulation to an adaptive pursuit of a set objective. Trajectory equations of motion are governed by,
mx" + Dcos(alfa) = 0 my" + Dsin(alfa) + mg = 0
where an atmospheric drag force and angle of attack are defined as,
D = .5*Cd*A*rho(h)*v^2 alfa = atan(vy/vx)
Let's examine the possibilities with a quick pseudo-code, setting up the blueprint for screening the solution strategies...
Quite ordinary at first glance until attempting to solve for a specific trajectory raises the question of how to coordinate the integrate and optimize modules to arrive at the solution. The "seamless" graphical environments suddenly fade into the sunset and reality sets in... you've been had!
Problems requiring collaborative manipulation of solution methods quickly draw out the deficiencies which marketers of various simulation wares are trying hard to obscure. Some of the most glaring:
The SDX solution clearly exhibits the absence of any such shortcomings. To underscore this point we searched unsuccessfully for alternate software solutions which are summed up in the competitors' corner.
Search for optimal trajectory
Note shadow trajectories due to evaluation of local Jacobian are
Competitors' corner -- It would be a useful comparison to present solutions applying different
tools to the same problem. However, both principal vendors failed to come up with one,
in contrast to their marketing claims of quick and easy solutions.
We've done the math -- now we invite you to check the calculations and then choose the best.