Re: solve a catenary (cosh) system
From: Jan C. Hoffmann (jch_at_arcore.de)
Date: 10/17/04
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Date: Sun, 17 Oct 2004 10:44:24 +0200
"FX" <fxfilias@esil.univ-mrs.fr> schrieb im Newsbeitrag
news:3273ua44dcmr@legacy...
>I try to solve a system or find the best approximation of the
> solution.
>
> I want to calculate a, c and d :
> y1= a*Cosh[x1/a + c]+d
> y2= a*Cosh[x2/a + c]+d
> y3= a*Cosh[x3/a + c]+d
>
> when given : x1,y1,x2,y2,x3 and y3.
>
> Up till now I can only find partial solutions with Taylor expansion.
>
Hi FX,
example using Newton Iteration:
a * cosh(x_1/a + c) + d - y_1 = 0
a * cosh(x_2/a + c) + d - y_2 = 0
a * cosh(x_3/a + c) + d - y_3 = 0
x_1 = 1
x_2 = 2
x_3 = 3
y_1 = 1
y_2 = 4
y_3 = 9
solution
a = 2.025661544
c = 1.068338482
d = -4.041957285
-- Regards/Gruss Jan C. Hoffmann
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