There is a slight energy gain because of the cycloidal movement, but is is less the the friction inherent in the system plus the wind resistance of the pendulum. Plus there is always energy lost converting momentum from one form to another, in this case rotary to linear.
What a great collection of videos! I've seen some of them as shortened clips, but this was much better. I have to note that the Little Squirt shown cutting through a chop at high speed had a unique control system. In addition to the attitude control system it used big brass balls in the throttle ...
There is a slight energy gain because of the cycloidal movement, but is is less the the friction inherent in the system plus the wind resistance of the pendulum. Plus there is always energy lost converting momentum from one form to another, in this case rotary to linear.