i study about electrodynamic tether system
i don't calculate current-voltage equation (OML Theory)
i understand how to calculate boundary conditions but i don't know how to intagrate equation directly
please give me some solution
I would suggest the following:
Differentiating the second equation of the first system (segment AB) with respect to ξ and substituting the derivative di/dξ from the first equation, we arrive at the differential equation d2φ/dξ2=3/4*φ1/2.
Next, trying a solution of the form φ=(aξ-b)k and substituting into the previous differential equation, we obtain k=4 and a=+-1/4. Then imposing the boundary condition φB=0, we arrive at the solution φ=((ξ- ξB)/4)4.
Then i is easily calculated by differentiating the last equation with respect to ξ, substituting into the second equation of the first system (segment AB), and solving trivially for i.
The second system (segment BC) may be treated similarly.
Woojae Jang I suggest reading this article Chapter A Brief Overview of Electrodynamic Tethers
No need for trial and error; the solution of d2φ/dξ2 = F'(φ) can be found immediately. It suffices to multiply by dφ/dξ and deduce that
(d/dξ)( (1/2)(dφ/dξ)2 - F(φ) ) = 0, which implies that
(1/2)(dφ/dξ)2 - F(φ(ξ)) = const (1/2)((i-1)2-F(φ(ξ))=const.
and take it on from there...
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