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[SOLVED] Solving a nonlinear equation

dwsmith

Well-known member
Feb 1, 2012
1,673
I let Mathematica run for over an hour but it couldn't solve this equation. Can someone run this in Matlab or Python and see if they can get a solution?

$\alpha = 2\arcsin\left(\sqrt{\frac{10014.6}{2*a}}\right)$
$\beta = 2\arcsin\left(\sqrt{\frac{10014.6 - 6339.06}{2*a}}\right)$

$$
780\sqrt{\frac{398600}{a^3}} = \alpha - \beta -(\sin(\alpha) - \sin(\beta))
$$
Solving for a.

Never mind. NSolve and Solve wont work but FindRoot did for {a,5000}.
 
Last edited:

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
I let Mathematica run for over an hour but it couldn't solve this equation. Can someone run this in Matlab or Python and see if they can get a solution?

$\alpha = 2\arcsin\left(\sqrt{\frac{10014.6}{2*a}}\right)$
$\beta = 2\arcsin\left(\sqrt{\frac{10014.6 - 6339.06}{2*a}}\right)$

$$
780\sqrt{\frac{398600}{a^3}} = \alpha - \beta -(\sin(\alpha) - \sin(\beta))
$$
Solving for a.

Never mind. NSolve and Solve wont work but FindRoot did for {a,5000}.
a=5000 is not a solution.
Graphing it with Wolfram suggests that it will only be zero if $a \to \infty$.
FindRoot is probably doing some rounding and truncation.
 

dwsmith

Well-known member
Feb 1, 2012
1,673
a=5000 is not a solution.
Graphing it with Wolfram suggests that it will only be zero if $a \to \infty$.
FindRoot is probably doing some rounding and truncation.
{a,5000} means look for a solution beyound 5000