This question popped up while trying to solve problem 7.41 from Taylor's Classical Mechanics book.(adsbygoogle = window.adsbygoogle || []).push({});

Basically we have the differential equation

[tex](1+4k^2\rho^2)\ddot{\rho} = \rho \omega^2 - 4k^2\rho{\dot{\rho}}^2-2gk\rho[/tex]

and we are looking if the equilibrium position [tex]\rho = 0[/tex] is stable.

After "linearizing" this you are supposed to end up with

[tex]\ddot{\rho} = (\omega^2 - 2gk)\rho[/tex]

but I really don't understand the correct way to arrive at this. Particularly, how are you supposed to justify dropping the [tex]4k^2\rho{\dot{\rho}}^2[/tex] term?

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# Linearizing a differential equation

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