
#1
Nov2212, 04:26 PM

P: 5

Hello!
I have a problem. How can I convert a left part from picture which is in coordinate system (r, s) to coordinate system (x, y) and then to coordinate system (ζ, η) (right part). I need Jacobian matrix because of integration some function above this region. Any helpful links or answers are welcome. 



#2
Nov2612, 11:25 AM

P: 280

Given a parametrization for your new coordinates (e.g. x=r cos(t), y=r sin(t), the new coordinates are:
[tex]\left(\begin{array}{cc}x'\\y'\end{array}\right)=det(Jacobian(x,y)) \left(\begin{array}{cc}x\\y\end{array}\right)[/tex] Where the Jacobian is merely: [tex]J=\left(\begin{array}{cc}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial t}\\\frac{\partial y}{\partial r}&\frac{\partial y}{\partial t}\end{array}\right)[/tex] 



#3
Dec112, 05:24 PM

P: 5

Thanks for answer.
Is parameter t in equation x = r cos(t) angle phi in the picture? 



#4
Dec312, 04:02 AM

P: 280

How change from one to another coordinate system
Yes, but this was the general formula. In your case, you are going from r,phi to x,y so you should take the inverse equations, i.e.
[tex]r=\sqrt(x^2+y^2) , t=atan(y/x)[/tex] You would then have r,t on the left hand side of the equation and the new Jacobian times x,y on the other one. 



#5
Dec312, 05:30 AM

P: 5

Ok. Thank you



Register to reply 
Related Discussions  
Convert this rectangular coordinate system point to spherical coordinate system  Calculus & Beyond Homework  1  
Tensor transformations for change of coordinate system  Linear & Abstract Algebra  4  
Change of Coordinate matrix  Calculus & Beyond Homework  1  
Coordinate system transform for antenna measuring system  Electrical Engineering  1  
Coordinate transformation and choice of a suitable coordinate system.  Special & General Relativity  2 