Need help to solve one differential equation

  • Thread starter TimJ
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  • #1
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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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!

Hi TimJ! Welcome to PF! :smile:

(have a theta: θ and an omega: ω :wink:)
[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 :wink:
 
  • #3
18
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Thank you for your help.
 

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