Matrix differentiation

2012 6 6
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0 个投票

Hi
I have matrix (3,3)in the form
M=[cos(a)*sin(b)*cos(c) sin(a)*sin(b)*sin(c) cos(a)^2*sin(b)^2*cos(c);.............;.......]
where a , b , c angls changing with the time
How i can differentiation the M according to time Mdott
Thx

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Andrei Bobrov
Andrei Bobrov 2012-6-6

1 个投票

syms a b c t
M=[cos(a)*sin(b)*cos(c) sin(a)*sin(b)*sin(c) cos(a)^2*sin(b)^2*cos(c)];
k = regexprep(char(M),{'\(a\)','\(b\)','\(c\)'},{'\(a\(t\)\)', '\(b\(t\)\)', '\(c\(t\)\)'});
out = feval(symengine,'diff', k, t)
ADD after rami's comment
z = feval(symengine,'diff', k, t);
out = sym(regexprep(char(z),'(\(t\))|(\*diff\([abc]\(t\), t\))',''))

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rami
rami 2012-6-6
Ok
As example
M=[cos(a)*sin(b)*cos(c) sin(a)*sin(b)*sin(c) cos(a)^2*sin(b)^2*cos(c);1 1 1;1 1 1];
k = regexprep(char(M),{'\(a\)','\(b\)','\(c\)'},{'\(a\(t\)\)', '\(b\(t\)\)', '\(c\(t\)\)'});
out = feval(symengine,'diff', k, t)
I have the result:
out =
[ cos(a(t))*cos(b(t))*cos(c(t))*diff(b(t), t) - cos(c(t))*sin(a(t))*sin(b(t))*diff(a(t), t) - cos(a(t))*sin(b(t))*sin(c(t))*diff(c(t), t), cos(a(t))*sin(b(t))*sin(c(t))*diff(a(t), t) + cos(b(t))*sin(a(t))*sin(c(t))*diff(b(t), t) + cos(c(t))*sin(a(t))*sin(b(t))*diff(c(t), t), 2*cos(b(t))*cos(c(t))*diff(b(t), t)*cos(a(t))^2*sin(b(t)) - sin(c(t))*diff(c(t), t)*cos(a(t))^2*sin(b(t))^2 - 2*cos(c(t))*sin(a(t))*diff(a(t), t)*cos(a(t))*sin(b(t))^2]
[ 0, 0, 0]
[ 0, 0, 0]
Is there any way to disappear the term diff(b(t), t),...

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更多回答（1 个）

Walter Roberson
Walter Roberson 2012-6-6

0 个投票

I am relatively sure the below should work:
syms a b c t
M=[cos(a(t))*sin(b(t))*cos(c(t)) sin(a(t))*sin(b(t))*sin(c(t)) cos(a(t))^2*sin(b(t))^2*cos(c(t));.............;.......]
diff(M, t)
What might also work, at least with sufficiently new Symbolic Toolbox, is
syms a(t) b(t) c(t) t
M=[cos(a)*sin(b)*cos(c) sin(a)*sin(b)*sin(c) cos(a)^2*sin(b)^2*cos(c);.............;.......]
diff(M,t)

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rami
rami 2012-6-6
syms a b c t
A=[cos(a(t))*sin(b(t))*sin(c(t)) sin(a(t))*cos(c(t)) 1;0 0 0;1 1 1]
diff(A, t)
Error in ==> POLEPLACEMENT at 9
A=[cos(a(t))*sin(b(t))*sin(c(t)) sin(a(t))*cos(c(t)) 1;0 0 0;1 1 1]
OR
syms a(t) b(t) c(t) t
M=[cos(a)*sin(b(t))*cos(c) sin(a(t))*sin(b(t))*sin(c(t)) cos(a(t))^2*sin(b(t))^2*cos(c(t));1 1 1;1 1 1];
diff(M, t)
Error in ==> POLEPLACEMENT at 12
syms a(t) b(t) c(t) t
rami
rami 2012-6-6
syms a(t) b(t) c(t) t
M=[cos(a)*sin(b)*cos(c) sin(a)*sin(b)*sin(c) cos(a)^2*sin(b)^2*cos(c);1 1 1;1 1 1];
diff(M, t)
??? Error using ==> syms at 61
Not a valid variable name.
Error in ==> POLEPLACEMENT at 12
syms a(t) b(t) c(t) t

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