Recent content by wrobel

Once again: this vector is the direction vector of the ball's rotation axis. The magnitude of this vector does not matter. The angle of rotation about this axis is given in #27.

Yes and It is not a surprise. If ##b = 0##, then the beetle is at rest, and thus the ball does not move. If, in the theorem cited in #29, the initial position coincides with the final position, then the axis of rotation is not defined uniquely .

The direction vector of the axis of the ball's rotation from its initial position to its final position is $$\left(\sqrt{(R/b)^2-1},0,1\right)^T$$ These coordinates are relative to the ##Oxyz## frame in the attachment UPD: This statement should be understood in the sense of the following...

It turns out that the system of ODEs in the attachment is integrable in closed form. Thus, the answer to the question is as follows: $$2\pi\left(1-\sqrt{1-\frac{mb^2(2J+mR^2)}{(J+mR^2)^2}}\right)$$

I just can't understand one thing: the equations of the ball's motion have already been derived. You can check this derivation out, and if you find it correct, you can solve these equations numerically and compare the results with your own hypotheses. Why don't you do this obviously rational thing?

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...