Hello, I have peculiar trouble with mathematica. I'm playing with lagrangians of some systems and I hit on "central problem". If I use my procedure in mathematica it solve 2 eq. of second order. But if you solve it by hand, you know, ##\phi## coord is "cyclic". And second eq. is reduced to ## \delta_t (mr^2 \phi)=0 ## and we introduce constant of angular momentum ##L##.(adsbygoogle = window.adsbygoogle || []).push({});

And the problem: If I let solve mathematica general equation without introduction ##L## I get another solution than if I transform second equation by introduction ##L##

(different eq.'s: ##2mr\phi'+mr^2\phi''=0## and ##mr^2\phi'=L##)

I used same initial condition.

Could you somebody advise where is the problem or how to resolve it?

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# Mathematica Mathematica NDSolve different solutions same eq's

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