anuttarasammyak's latest activity

The insect moving around the latitude circle has angular momentum both in the z-direction and in the direction normal to the latitude...

We draw latitude lines and longitude lines on the globe and set it in a recess for the free rotation with the north pole top initially...

As for movements with regard to trajectory circle, the cases : a. a bettle spins at the circle center b. long snake forms a ring shape...

But in OP a priori I observe this such that condition decides the axis of rotations both beetle and the globe as posted #4. Say beetle...

The rotation axis is the line on which the center of the ball and the center of beetle trajectory circle are. Do I mistreat degree of...

Conservation of angular momentum $$I_G\omega_G+I_B\omega_B=0$$ The bug returns to the start mark with period...

This anti-symmetric equation has six non-zero solutions.

Under a coordinate transformation ##x^{\mu}\to x'^{\mu}=f^{\mu}(x)##, the two metrics transform as $$g'^{\alpha\beta}=\frac{\partial...

Thank you @Demystifier 1. I observe that a. ## \bar{g}_{\mu\nu}-g_{\mu\nu}## transforms as a covariant tensor under coordinate...

I should appreciate it if you could teach me how to verify it.

Thank you, @Demystifier. In general, the difference of two tensors is again a tensor. However, in the context of variations of the...

I believe there is no such quantity, because you study a variation of the object that defines the covariant and contravariant components.

You forgot to put double dollar signs at head and tail of the equalion lines. I put them. ------------ Has any one any idea to solve...

It is a tensor whose covariant and contravariant components are ##\delta g_{\mu\nu}## and ##-\delta g^{\mu\nu}##, respectively...

3. is just a definition of the dual tensor, i.e. the rule how to raise indices in the same world. In 2. you try to compare quantities...