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Need help to solve one differential equation

by TimJ
Tags: differential, equation, solve
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TimJ
#1
Apr6-09, 02:31 PM
P: 18
Does anybody know how to solve this differential equation:

[tex]
\frac{d^2 \theta}{dt^2}-A\sin(\theta)-
\frac{B^2 \cos(\theta)}{ \sin^3(\theta) }=0
[/tex]

This is an equation that i get from the brachistochronic motion on the surface of a sphere.
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tiny-tim
#2
Apr6-09, 06:06 PM
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tiny-tim's Avatar
P: 26,157
Hi TimJ! Welcome to PF!

(have a theta: θ and an omega: ω )
Quote Quote by TimJ View Post
[tex]
\frac{d^2 \theta}{dt^2}-A\sin(\theta)-
\frac{B^2 \cos(\theta)}{ \sin^3(\theta) }=0
[/tex]
Try writing d2θ/dt2 = dω/dt = dω/dθ dθ/dt = ω dω/dθ = 1/2 d(ω2)dθ,

so d(ω2)/dθ = 2Asinθ + 2Bcotθcosec2θ
TimJ
#3
Apr7-09, 03:41 AM
P: 18
Thank you for your help.


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