We know that Bí = Rik Bu Bk What about J; how does that transform under rotations? I will show that - transforms as a vector", i.e., in the same way as B does; Di = Rij Vj. 'cosø -sinf For simplicity, consider 2D: = 2 ox ) ; X = RX, with R = want to We want = to find: ax' ه ای را به ایمی sing cosø Use the chain rule, eg: af = ax' of ax ах дух af ду ag ax' ก 器 22 را = R11 af ду + R12 0774
We know that Bí = Rik Bu Bk What about J; how does that transform under rotations? I will show that - transforms as a vector", i.e., in the same way as B does; Di = Rij Vj. 'cosø -sinf For simplicity, consider 2D: = 2 ox ) ; X = RX, with R = want to We want = to find: ax' ه ای را به ایمی sing cosø Use the chain rule, eg: af = ax' of ax ах дух af ду ag ax' ก 器 22 را = R11 af ду + R12 0774
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Explain in detail why the line circled in red is true
Transcribed Image Text:We know that Bí
=
Rik Bu
Bk
What about J; how does that transform
under rotations?
I will show that - transforms
as
a vector", i.e., in the same way
as
B does; Di
=
Rij Vj.
'cosø -sinf
For simplicity, consider 2D:
=
2
ox
) ; X = RX, with R =
want to
We want
=
to find:
ax'
ه ای را به ایمی
sing cosø
Use the chain rule, eg:
af
=
ax'
of ax
ах дух
af ду
ag ax'
ก
器
22
را
=
R11
af
ду
+ R12 0774
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