[Scilab-users] RE(2): finding roots

[Rafael Guerra]

Mike,

Thanks for the explanation; it is amazing to learn that such odd equation arises from a physical problem.

     cos(x) * cosh(x) = -1
or:
    (exp(i​x)+​exp(​-ix))/2 * (exp(x)+exp(‑x))/2  = -1

Best regards
Rafael

-----Original Message-----
From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Michael J. McCann
Sent: Monday, March 31, 2014 9:46 AM
To: International users mailing list for Scilab.
Subject: Re: [Scilab-users] RE(2): finding roots

Someone asked about the reason for looking for the roots. In case the original question didn't get answered, or the problem has been changed, the problem arises in getting the eigenfunctions (natural mode shapes) for a cantilevered, built in vibrating uniform rod (or beam).  After the first two the rest come very close to (2*n+1)pi/2 because cosh(x) gets so big that only when cos(x) is virtually zero does the solution appear.
Mike.
=========
On 30/03/2014 21:55, Paul CARRICO wrote:
> Thanks ... indeed much more stable ..
>
> Paul
>
> -----Message d'origine-----
> De : users [mailto:users-bounces at lists.scilab.org] De la part de 
> Rafael Guerra Envoyé : dimanche 30 mars 2014 23:34 À : 'International 
> users mailing list for Scilab.'
> Objet : [Scilab-users] RE(2): finding roots
>
> Hi Paul,
>
> The new code here below does not show any such problem for all N solutions I tried.
> Note that your problem: cos(x) .* cosh(x) + 1 = 0; is equivalent to: cos(x) + sech(x) = 0.
> The latter form seems to be numerically more stable.
>
> Regards,
> Rafael
> .............
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