how can i rewrite an equation base on variables

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dear all
i have 3*1 matrix like matrix E below
syms qd td ed q teta
E =[ ed*cos(q)*sin(teta) - cos(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - td*sin(q)*sin(teta)^2 ; cos(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta)) + ed*sin(q)*sin(teta) + td*cos(q)*sin(teta)^2 ; ed*cos(teta) + cos(q)*sin(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - sin(q)*sin(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta))]
that i want to rewrite it in [3*3]*[qd;td;ed]=[E] this form
is there any Command that can help me to calculate this [3*3] matrix by matlab
answer should be like this:
[ -cos(q)*cos(teta)*sin(teta), - cos(teta)^2*sin(q) - sin(q)*sin(teta)^2, cos(q)*sin(teta)]
[ -cos(teta)*sin(q)*sin(teta), sin(q)*cos(teta)^2 + cos(q)*sin(teta)^2, sin(q)*sin(teta)]
[ cos(q)^2*sin(teta)^2 + sin(q)^2*sin(teta)^2, cos(q)*cos(teta)*sin(q)*sin(teta) - cos(teta)*sin(q)^2*sin(teta), cos(teta)]
i really apreciated if you could help me

Accepted Answer

Birdman
Birdman on 9 Dec 2017
Try the following code:
syms qd td ed q teta
E =[ ed*cos(q)*sin(teta) - cos(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - td*sin(q)*sin(teta)^2 ; cos(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta)) + ed*sin(q)*sin(teta) + td*cos(q)*sin(teta)^2 ; ed*cos(teta) + cos(q)*sin(teta)*(qd*cos(q)*sin(teta) + td*cos(teta)*sin(q)) - sin(q)*sin(teta)*(td*cos(teta)*sin(q) - qd*sin(q)*sin(teta))]
Ecollected=collect(E,[qd,td,ed])
for i=1:size(E,1)
E3by3form(i,:)=coeffs(Ecollected(i),[qd,td,ed])
end
Let me know the results. The answer you want is stored in E3by3form.
  5 Comments
Walter Roberson
Walter Roberson on 22 Dec 2017
That cannot be solved.
x = sym('x',[1 6]);
consnt7(x)
ans(:,:,1) =
[ 0, 0, 0]
[ 0, 0, 0]
[ 0, 0, 0]
ans(:,:,2) =
[ 0, -sin(x1), cos(x1)*sin(x2)]
[ 0, cos(x1), sin(x1)*sin(x2)]
[ 1, 0, cos(x2)]
The first pane of the 3D answers can be solved, as it is already all 0. However, in the second pane, ans(:,:,2), there is no x1 such that -sin(x1) == 0 at the same time that cos(x1) == 0 -- and even if there were, the 1 in the bottom left corner, position ans(3,1,2), can never be equal to 0, so there is no possible input vector such that the result of the function is all zeros.

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