In some texts on classical mechanics and not only, the Euler--Lagrange equations of motion are directly obtained as solution of variational problems. On the other side, sometimes reading about ...
Do you think that symplectic reduction (Marsden Weinstein reduction) is interesting from a physical point of view? If so, why? Does it give you some new physical insights? There are some possible ...
Has the dynamics of billiards in a polygon subject to gravity been studied? What I have in mind is something like this: Still Snell's ...
Here is a version of Bertrand theorem. Let us consider a force $F(r)$ which depends only on the distance to a given point. If all trajectories which remain bounded are closed, then either $F(r)=ar$ ...
Can the equation of motion with friction be written as Euler-Lagrange equation, and does it have a quantum version?
My (non-expert) impression is that many physically important equations of motion can be obtained as Euler-Lagrange equations. For example in quantum fields theories and in quantum mechanics quantum ...
What is the shortest length of string that suffices to hang a unit-radius ball $B$? This question is related to an earlier MO question, but I think different. Assume that the ball is ...
Wikipedia says that, "The oloid is one of the only known objects, along with some members of the sphericon family, that while rolling, develops its entire surface." Below are illustrations of ...
This should be true in a more general setting, but for simplicity consider billiards that are connected, compact subsets of the plane with boundary $C^2$ except at finitely many points. A ball (or a ...
Periodic orbits of a billiard ball bouncing in a square have been well-studied. I am seeking similar analysis of what is sometimes called a rough ball, one whose high friction causes it to pick up ...