
Re: Symbolic Toolbox: Solution of Trigonometric Equations
Posted:
Jun 15, 2013 4:13 AM


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

