Matrix differentiation

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

Answer 1

[Andrei Bobrov]

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\))',''))

[rami]

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),...

Answer 2

[Walter Roberson]

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)

[rami]

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]

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