Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have an equation of the form;

[tex]

\frac{d}{dt}(W) = \omega \left(x \frac{\partial}{\partial y} - y \frac{\partial}{\partial x} \right) W + g \frac{\partial}{\partial y} W + k x \frac{\partial^2}{\partial y^2} W

[/tex]

I want to change it into the rotating frame using the transform;

x = x' cos(wt) - y' sin(wt)

y = x' sin(wt) + y' cos(wt)

I have calculated the derivatives of these transforms to be;

[tex]

\frac{\partial}{\partial x} = -cos(\omega t) \frac{\partial}{\partial x'} - sin(\omega t) \frac{\partial}{\partial y'}

\\

\frac{\partial}{\partial y} = -cos(\omega t) \frac{\partial}{\partial y'} + sin(\omega t) \frac{\partial}{\partial x'}

\\

\frac{\partial^2}{\partial x^2} = -cos^(2)(\omega t) \frac{\partial^2}{\partial x'^2} - sin^(2)(\omega t) \frac{\partial^2}{\partial y'^2}

[/tex]

I am assuming I can just substitute these transforms for x, y and their derivatives into the original equation and this will give me the original equation in the rotating frame...but do I have to do something with the time derivative on the L.H.S of the original equation??

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transform a pde into rotating frame

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**