Replace x with x(t) in a symbolic matrix

Hello,

I have a 3x3 symbolic matrix T1. I want to replace theta1 with theta1(t), theta2 with theta2(t) in my matrix. I tried using the subs function like so

syms theta1 theta2 theta3

AT1 = subs(T1, {theta1, theta2, theta3},...
  {theta1(t), theta2(t), theta3(t)})


%--------------- My T1 is----------- 
[  cos(theta1 + theta2 + theta3), sin(theta1 + theta2 + theta3), 0,   8*cos(theta1 + theta2 + theta3) + 5*cos(theta1 + theta2) + 10*cos(theta1)]
[ -sin(theta1 + theta2 + theta3), cos(theta1 + theta2 + theta3), 0, - 8*sin(theta1 + theta2 + theta3) - 5*sin(theta1 + theta2) - 10*sin(theta1)]
[                              0,                             0, 1,                                                                           0]
[                              0,                             0, 0,                                                                           1]

but matlab expects an arithmetic expression as the input function in "subs", hence throws an error.

A workaround I thought of, was calling elements individually and converting them, but however I try an error shows up when I use brackets. By which I mean 'theta1' can be replaced by 'theta4' but not 'theta4(t)'.

In the end I need to differentiate T1, so theta has to be theta(t) for "diff" function to work properly

Please let me know how I can solve this issue.

PS: It is also fine if there is some way I can call elements of the matrix below, but I don't think it is possible

>> T10
 
T10(t) =
 
[  cos(theta1(t)), sin(theta1(t)), 0,  10*cos(theta1(t))]
[ -sin(theta1(t)), cos(theta1(t)), 0, -10*sin(theta1(t))]
[               0,              0, 1,                  0]
[               0,              0, 0,                  1]

Thanks,

Venkatesh.

Answer 1

[Walter Roberson]

syms theta1 theta2 theta3
T = [  cos(theta1 + theta2 + theta3), sin(theta1 + theta2 + theta3), 0,   8*cos(theta1 + theta2 + theta3) + 5*cos(theta1 + theta2) + 10*cos(theta1)
    -sin(theta1 + theta2 + theta3), cos(theta1 + theta2 + theta3), 0, - 8*sin(theta1 + theta2 + theta3) - 5*sin(theta1 + theta2) - 10*sin(theta1)
    0,                             0, 1,                                                                           0
    0,                             0, 0,                                                                           1];

syms theta4(t) theta5(t) theta6(t)
temp = subs(T, {theta1, theta2, theta3}, {theta4, theta5, theta6});
syms theta1(t) theta2(t) theta3(t)
AT1 = subs(temp, {theta4, theta5, theta6}, {theta1, theta2, theta3});

"It is also fine if there is some way I can call elements of the matrix below,"

T10(t) =

[ cos(theta1(t)), sin(theta1(t)), 0, 10*cos(theta1(t))]

That is not a matrix: it is a symbolic function that returns a matrix. You cannot access individual elements of the function through normal indexing. You can, however, use formula(T10) which will return an array result that is not a function, and then you can index the array result.

[Venkatesh Sripada]

Hello Walter,

Thank you very much. This explanation is very clear and self explanatory. My question above has been answered.

I would also like to ask if there is matlab function that separates out the differentials from the matrix i.e

diff(AT1)
 
ans =
 
[   10*cos(theta1(t))*diff(theta1(t), t) + 8*cos(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t)) + 5*cos(theta1(t) + theta2(t))*(diff(theta1(t), t) + diff(theta2(t), t)),   8*cos(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t)) + 5*cos(theta1(t) + theta2(t))*(diff(theta1(t), t) + diff(theta2(t), t)),  8*cos(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t))]
[ - 10*sin(theta1(t))*diff(theta1(t), t) - 8*sin(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t)) - 5*sin(theta1(t) + theta2(t))*(diff(theta1(t), t) + diff(theta2(t), t)), - 8*sin(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t)) - 5*sin(theta1(t) + theta2(t))*(diff(theta1(t), t) + diff(theta2(t), t)), -8*sin(theta1(t) + theta2(t) + theta3(t))*(diff(theta1(t), t) + diff(theta2(t), t) + diff(theta3(t), t))]
[                                                                                                                                                                                                                         0,                                                                                                                                                                                  0,                                                                                                        0]
 

differential of my final AT1 gives me this huge matrix. Can I separate out diff(theta1(t), t); diff(theta2(t), t) and diff(theta3(t), t) into a column matrix?

Thanks,

Venkatesh.

[Walter Roberson]

If you are looking at seperating out those things, then I recommend that you have a look at odeFunction() and the workflow shown in the first example, including odeToVectorField

[Venkatesh Sripada]

Will look into. Thank you very much