Recent content by wrobel

Something like that, yeah

I saw the following question somewhere on the forum—I don't remember which thread exactly—and I think it even went unanswered. Consider a manifold ##M## with local coordinates ##t=(t^1,\ldots,t^m)##, equipped with a symmetric connection ##\Gamma_{ij}^k(t)##. What sufficient conditions must be...

I apologize, I didn't realize right away that the constraint is holonomic, so the problem isn't of any interest.

Here is another interesting problem. A planar rigid body of mass ##m## moves in a plane. Let ##S## denote the center of mass of the body. Let us fix a point ##A## in the body such that ##|AS| = b > 0##. Let ##J## denote the moment of inertia of the body about the axis passing through point ##S##...

Gemini said that my proof was full of errors. In the course of our further conversation, I convinced it that there were no errors. But you can convince an AI of anything, which is why I created this thread. Unfortunately, I deleted that chat.

In the literature, I have only seen one interpretation of these words: for any constant c the statement 'f(x)=c a.e. ' is wrong. See for example Eigenvalue theorems in topological transformation groups

For a lecture, I needed to state and prove a lemma. See the text. I wrote the proof and just ran it through an AI for good measure. And then all hell broke loose! :) Did I actually write an incorrect proof?

Chaos is an informal umbrella term for a broad spectrum of fundamentally distinct dynamical phenomena that manifest in the complex behavior of trajectories within a dynamical system. Both what constitutes 'complex behavior' and how 'chaos' is defined must be rigorously specified in each case...

outline of a solution

Once again: the system has two degrees of freedom — two independent generalized coordinates.

The system has two degrees of freedom

the initial post is updated

A uniform massive cylinder is free to rotate about its fixed horizontal axis. A uniform disk of smaller radius rolls without slipping along the inner surface of the cylinder. The system is in the uniform gravitational field g. Prove that any motion of the system starting from rest is periodic...

Is it possible to teach at a US high school with just a university degree?

I don't know about where you are, but in RF someone with a university degree can start teaching at a school after a short training course, and they'll actually be quite valued there. It's just a Plan B.