Orthogonality from infinitesimal small rotation

[Warlord_]

Hello buddies,

Could someone please help me to understand where the second and the third equalities came from?
Thanks,

 

[DEvens]

Um... Ok, it's a little difficult to know what level of detail you want.

The first equation essentially says that the length of a vector does not change under rotations. The second one follows from the first one using the chain rule, and assuming delta of gik is zero.

 

[Warlord_]

Thanks for answering,

gik is basically the inner product of the base set vector, i.e., <ei,ek>.
- Could you please explicit the chain rule?
- is vik time dependent? And since it is an infinitely small matrix, the $\delta v^k_i = I$?

Thanks