A Problem in Lagrangian Mechanics
Today, as well as saying goodbye to Sally Church, I managed to finish my lecture course on Theoretical Physics. There’s still another week of teaching to go, but I have covered all the syllabus now and can use the remaining sessions for revision. The last bit of the course module concerned the calculus of variations and a brief introduction to Lagrangian mechanics so for a bit of fun I included this example.
Professor Percy Poindexter of the University of Neasden has invented a new theory of mechanics in which the one-dimensional motion of a particle in a potential is governed by a Lagrangian of the form
Use Hamilton’s Principle and an appropriate form of the Euler equation to derive the equation of motion for such a particle and comment on your answer.
UPDATE: Since nobody has commented I’ll just reveal the point of this question, which is that if you follow the instructions the equation of motion you should obtain is
which is exactly the same as you would have got using the usual Lagrangian
Anyone care to comment on that?