This video is an introduction to trajectory optimization, with a special focus on direct collocation methods. The slides are from a presentation that I gave at Cornell, linked here:

http://www.matthewpeterkelly.com/tuto...

The journal paper version of this talk, to be published by SIAM Review in December 2017:

http://www.matthewpeterkelly.com/rese...

The derivation of the cart-pol dynamics can be found here:

http://www.matthewpeterkelly.com/tuto...

My general tutorial page for trajectory optimization is:

http://www.matthewpeterkelly.com/tuto...