# [SOLVED]Solving a nonlinear equation

#### dwsmith

##### Well-known member
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
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
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