# How change from one to another coordinate system

by soks
Tags: coordinate
 P: 280 Given a parametrization for your new coordinates (e.g. x=r cos(t), y=r sin(t), the new coordinates are: $$\left(\begin{array}{cc}x'\\y'\end{array}\right)=det(Jacobian(x,y)) \left(\begin{array}{cc}x\\y\end{array}\right)$$ Where the Jacobian is merely: $$J=\left(\begin{array}{cc}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial t}\\\frac{\partial y}{\partial r}&\frac{\partial y}{\partial t}\end{array}\right)$$
 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. $$r=\sqrt(x^2+y^2) , t=atan(y/x)$$ 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.