- #1
adamwitt
- 25
- 0
Hi,
I need some help understanding the solution to a problem.
Equations:
x = r.cos(θ)
y = r.sin(θ)
r = x2 + y2
theta = arctan(y/x)Question:
Determine the Jacobian Matrix for (x,y)T and for (r, θ)T
SOLUTION:
I understand and can compute by myself the Jacobian for (x,y)T, but the solution to for J(r, θ) i don't understand.
J(r,θ) = ( (@r/@x, @r/@y) , (@θ/@x, @θ,@y) )T
Ok so that makes sense...
Then they gave me this...
(@r/@x, @r/@y) =( x / sqrt( x2 + y2 ) , y / sqrt(x2 + y2) )
Why isn't it just 2x and 2y respectively? why does it resemble something similar to a magnitude?
thanks for your help.
I need some help understanding the solution to a problem.
Equations:
x = r.cos(θ)
y = r.sin(θ)
r = x2 + y2
theta = arctan(y/x)Question:
Determine the Jacobian Matrix for (x,y)T and for (r, θ)T
SOLUTION:
I understand and can compute by myself the Jacobian for (x,y)T, but the solution to for J(r, θ) i don't understand.
J(r,θ) = ( (@r/@x, @r/@y) , (@θ/@x, @θ,@y) )T
Ok so that makes sense...
Then they gave me this...
(@r/@x, @r/@y) =( x / sqrt( x2 + y2 ) , y / sqrt(x2 + y2) )
Why isn't it just 2x and 2y respectively? why does it resemble something similar to a magnitude?
thanks for your help.