Another worked Landau pendulum problem
Posted by peeterjoot on July 14, 2012
Question: Pendulum with support moving in line
This problem like the last, but with the point of suspension moving in a horizontal line .
Our mass point has coordinates
so that the velocity is
Our squared velocity is
In the last term, we can reduce the sum of sines, finding a total derivative term and a remainder as in the previous problem. That is
Putting all the pieces together and dropping the total derivatives we have the stated solution
 LD Landau and EM Lifshitz. Mechanics, vol. 1. 1976.