Recent content by wrobel

text: normal distribution, abnormal distribution, paranormal distribution, normal distribution inside a boa constrictor

The angular velocity of a rigid body is defined by the Euler formula: $$\boldsymbol{v}_A=\boldsymbol v_B+\boldsymbol\omega\times\boldsymbol{BA}.\qquad(*)$$ The vector ##\boldsymbol\omega## can depend on time, but it is independent of any spatial variables. And, indeed, if ##\boldsymbol v## is a...

I am confident that this theorem is not new. Its proof relies heavily on Zorn's lemma, which is also not surprising

Hi everyone, I would like to share a result regarding the existence of solutions for systems of ordinary differential equations with an arbitrary number of variables. Let ##\Gamma## be an arbitrary nonempty set of indices. For each ##\gamma \in \Gamma##, let ##f_\gamma## be a scalar-valued...

I’m reposting a question from MathOverflow here. I’d love to hear your thoughts/comments on it. https://mathoverflow.net/questions/509562/nonautonomous-lie-derivative the problem is solved

I fed my English translation of this problem (from the initial post) to an AI. It correctly recognized it as problem number 2.1.51 from Savchenko, but then provided an incorrect solution and the wrong answer. Some people, to put it mildly, somewhat overestimate the omnipotence of this thing I guess.

????? By definition, purely translational motion is when all the points of a rigid body move with the same velocity

My version is $$L=mr^2\dot\theta^2(1+\cos\alpha)+mgr\theta\sin\alpha$$ hopefully that is the same:)

A slab rests on two massless rollers of different radii such that the angle of the slab's inclination is ##\alpha##. There is no slipping between the slab and the rollers, nor between the rollers and the ground. Prove that the slab moves with purely translational motion and find its...

Any set can be covered by a finite intersection of closed sets; simply take its closure. Furthermore, the closure of a set is itself the intersection of all closed sets containing it.

mech problems I like 3D problems more, but these are also great

Almost always, the field of scalars is the field of real or complex numbers.

The book is pointless. The author yanked random bits from differential geometry, linear algebra, calculus, and physics. It’s the best way to make sure the reader ends up understanding absolutely nothing.

"No forces" and "zero net force" are in fact the same thing, since we are considering a single particle. If you have a particle at rest in an inertial frame, you can not distinguish one case from another

Do that. will see how GPT deals with it