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I am struggling with this tutorial problem: If you have the following lagrangian:

L = m/2(aX^2 + bXY + cY^2) - K/2(ax^2 + bxy + cy^2)

(Where captial letters indicate first derivative with respect to time, a,b,c constants)

What physical system does it represent?

It looks like a simple coupled oscillator, but I dont know what the extra velocity term (bXY) could represent? Any help would be much appreciated.

Thanks