MHB Put the 2D nonlinear system into Polar Coordinates

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The discussion focuses on converting a 2D nonlinear system into polar coordinates, resulting in the equations r′ = r(r^2 − 4) and θ′ = x′1 = x1 − x2 − x1^3, x′2 = x1 + x2 − x2^3. Participants are encouraged to share their progress or initial thoughts to facilitate effective assistance. This approach helps helpers avoid suggesting solutions that the poster may have already attempted. The emphasis is on collaboration and clarity in the problem-solving process. Engaging in this manner enhances the overall learning experience.
Krish23
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Show that, in polar coordinates, the system is given by
r′ = r(r^2 − 4)
θ′ = 1x′1 = x1 − x2 − x1^3
x′2 = x1 + x2 − x2^3
 
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Hello and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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