Difficult Problems in Classical Mechanics

[SpaceWalrus]

My professor for classical mechanics has asked that we find some difficult problems in classical and solve them. My first thought was to look through my book for hard problems. However, we are using a free PDF that is rather lackluster when it comes to homework problems. Almost all of the questions are trivial, and amount to solving for the equations of motion once I have set up the Hamiltonian. I have a copy of VI Arnold's Mathematical Methods of Classical Mechanics on hand. Though I haven't had too much time to peruse it for interesting problems, it appears to be hands-off and not provide many problems.

I currently know the basics of Hamiltonian's and anything below that. Does anyone have any advice where I can find interesting and sufficiently difficult problems in classical to solve? If anyone has any problems of their own, I would love to hear those too.

 

[marcusl]

Look in your school library. Both Goldstein's and Landau's texts on classical mechanics will have challenging problems.

 

[Bob S]

Here is a very challenging problem using calculus of variations. A frictionless bead slides on a smooth stiff wire from a fixed upper point x1, y1 to a fixed lower point x2, y2; y2 < y1, x2 ≠ x1 under gravitational force. Find the shape of the curve in the wire such that the transit time is a minimum.

 

[lugita15]

David Morin's Classical Mechanics book has a great wealth of interesting and challenging problems.

 

[lugita15]

Here is a very challenging problem using calculus of variations. A frictionless bead slides on a smooth stiff wire from a fixed upper point x1, y1 to a fixed lower point x2, y2; y2 < y1, x2 ≠ x1 under gravitational force. Find the shape of the curve in the wire such that the transit time is a minimum.

Historically, of course, the brachistochrone problem was very challenging. But nowadays, isn't it a trivial calculus of variations exercise?