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Re: Symbolic Toolbox: Solution of Trigonometric Equations
Posted:
Jun 15, 2013 4:13 AM
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On 6/15/2013 1:45 AM, Dinesh Bhati wrote:
> Can you please help in the following particular case. I want all the minima points.
>Toolbox is returning only one.I have plotted function 'p'. It has no. of minimas.
>
> syms t10 t11
> p=(cos(t11)*sin(t10) + sin(t10)^3*cos(t11)*+sin(t10)^2 - cos(t11)^2*sin(t10)^2);
> eq1=diff(p,t10);
> eq2=diff(p,t11);
> s=solve(eq1,eq2,'t10','t11')
> s.t10
> s.t11
There are a little more to it. You might be better of either do it
by hand, or find a ready to use code, or write one yourself.
May be file exchange has something. (or toolbox might allready have
one, do not know)
But here is a sketch of algorithm:
given: f(x,y)
1) find diff(f,x) and diff(f,y)
2) find solution to diff(f,x)=0. let sol be yi and xi
3) replace y in diff(f,y) by yi. Now solve diff(f,y)=0 for xj
4) just found critical point(s) (xj,yi)
5) now replace x in diff(f,y) by xi from (2) and solve diff(f,y)=0 for yj
6) found another critical point(s) (xi,yj)
7) check each point if min/max/saddle points using second derivatives.
--Nasser
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