Fly a 747 using MATLAB

Animate the motion of a 747 along a helical path all from within MATLAB.

In this demo, we walk through the steps of animating the 3D motion of a 747 aircraft given a helical trajectory described in parametric form. The challenge is to make the aircraft move such that its axis of symmetry is always pointing along the velocity vector. By reducing the problem to circular motion, we devise a strategy by which we are able to do the same. However, when we extrapolate the solution to the actual trajectory, we see that the aircraft does a "mysterious" 360 degree flip at well-defined points in the trajectory much like the manner in which the pilot did for the first test flight for the 747.
Can you figure out the loophole in this strategy and correct the code to eliminate this flip?

The video that walks through the steps of building this demo from scratch are here under the "Aerospace Application Examples" section:

Several enhancements have been made to the demo. See this submission:

http://www.mathworks.com/matlabcentral/fileexchange/27986