Recent content by wrobel

I think that the case when the mass distribution on the circle has rotational symmetry is completely different from the case when it does not

The angular velocity of the ball changes its direction relative to the ball-fixed frame (see the text attached) and thus it changes its direction relative to the lab frame. Thus, there is no fixed axis about which the ball rotates.

This contradicts the formulas attached.

here is my analysis

It's a bit funny because I have equations written down and you're just saying words :)

No!

This does not follow from anything. The ball is a rigid body with a fixed point, and thus it has three degrees of freedom. It is not obliged a priori to rotate about a fixed axis.

The ball has three degrees of freedom

Text: 1) Let's solve a physics problem. There is a block hung on a string. A bullet shoots straight through the block and loses half of its speed... 2) Do you have any tasks about a little squirrel and nuts, please? 3) Sure! There is a little squirrel hung on a string... ps No squirrels...

I composed a problem and initially thought it could be solved by purely analytical means, but it turns out it cannot. The problem is as follows: a homogeneous ball of radius ##R## can rotate freely about its fixed center ##O##. Let ##J## denote its moment of inertia relative to an axis passing...

I would like to share a concise proof of the Poincaré Lemma Theorem (Poincaré Lemma) Assume that a smooth ##k##-form (##k\in\mathbb{N}##) $$\omega = \sum_{i_1 < \dots < i_k} \omega_{i_1 \dots i_k} (x) dx^{i_1} \wedge \dots \wedge dx^{i_k}$$ is defined in a neighbourhood of the origin in...

I haven't checked it out myself, but I trust you.

1. Transport of Differential Forms Let ##M## be a smooth manifold with local coordinates ##x=(x^{1},\dots,x^{m})^{T}##. Consider a ##k##-form ##\omega## depending on ##t##: $$\omega(t,x) = \sum_{i_{1}<\dots<i_{k}} \omega_{i_{1}\dots i_{k}}(t,x) dx^{i_{1}} \wedge \dots \wedge dx^{i_{k}}$$ Let...

No, I haven't seen this paper. Thank you. I’m not an expert in algorithm theory and math. logic, but it seems he is addressing a scientific question and has obtained a new result. My goal is much more modest: it is purely educational and methodological

The goal of this post is to formally construct the theory of elementary functions without gaps, from the perspective of a university-level analysis course. It is intended as a unifying overview for undergraduate students who have previously encountered these functions in school but perhaps...