wrobel's latest activity

An original formulation of the problem and a picture are strongly needed.

A disk of radius ##r## is wrapped with an inextensible massless string. A particle of mass ##m## is attached to the end of the string...

Sometimes students think that a mass point can move along a potential line. In general It is not so.

for what purpose, if I may ask?

I would assume that the bottom of the rod can slide along a horizontal line without friction. Then I would answer the problem's...

Actually not. Moreover in most cases it is counterproductive.

Hello Intellectuals! So far it seems to be reasonable to learn mathematics in a rigorous way by not solely considering the techniques of...

I have seen several attempts to adapt Lagrangian formalism for variable mass systems. In my opinion all of them failed. Actually I think...

These examples show possible obstacles to extending coordinate charts.

for example ##(1,2)## and ##(3,4)## then ##(1,\sqrt 2)## and ##(\sqrt 2,1)##

O, it seems I understand the question. Consider a torus ##\mathbb{T}^2## with angle coordinates ##(\psi_1,\psi_2),\quad...

you can cover a manifold with a single chart if only this manifold is diffeomorphic to an open subset of ##\mathbb{R}^m##. I do not...

this is essentially the same standard proof that everybody knows

Nice way to prove the law of sines but what about to get ##2R## in the same spirit? :)

Most funny thing is that the system is Hamiltonian (see #18). Even the "energy" integral exists: $$\frac{1}{2}\dot...