Why is the derivative of a matrix not of the same order?

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Farzad Torabi 2022-11-15

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回答： Walter Roberson 2022-11-17

采纳的回答： Star Strider

I need to take the derivative of the "Q" matrix of joints in Matlab for a robot. but using the derivative method here

https://de.mathworks.com/help/matlab/ref/diff.html

I see that the derivative of a 3x3 matrix is a 2x3 matrix! why? should it be so?

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Farzad Torabi 2022-11-15

Thank you very much for your point

Les Beckham 2022-11-16

You are quite welcome.

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Star Strider 2022-11-15

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Use the gradient function instead of diff.

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Farzad Torabi 2022-11-15

It worked!! Many Thanks!!!

Star Strider 2022-11-15

As always, my pleasure!

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Walter Roberson 2022-11-17

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在 MATLAB Online 中打开

For the case where rotations are no rotations in z, but there are two joints moving around

and

with angular rotational velocities

and

syms x y z t alpha_1 alpha_2 cx_1 cy_1 cz_1 cx_2 cy_2 cz_2 theta theta_1 theta_2

R = @(theta) [cos(theta) sin(theta) 0 0; -sin(theta) cos(theta) 0 0; 0 0 1 0; 0 0 0 1]

R = function_handle with value:

@(theta)[cos(theta),sin(theta),0,0;-sin(theta),cos(theta),0,0;0,0,1,0;0,0,0,1]

T = @(tx, ty, tz) [1 0 0 tx; 0 1 0 ty; 0 0 1 tz; 0 0 0 1]

T = function_handle with value:

@(tx,ty,tz)[1,0,0,tx;0,1,0,ty;0,0,1,tz;0,0,0,1]

RotAround = @(theta, cx, cy, cz) T(-cx, -cy, -cz) * R(theta) * T(cx, cy, cz)

RotAround = function_handle with value:

@(theta,cx,cy,cz)T(-cx,-cy,-cz)*R(theta)*T(cx,cy,cz)

Q1 = RotAround(theta_1 + alpha_1 * t, cx_1, cy_1, cz_1)

Q1 =

Q2 = RotAround(theta_2 + alpha_2 * t, cx_2, cy_2, cz_2)

Q2 =

Q = simplify(Q1 * Q2)

Q =

eqns = Q*[x;y;z;0]

eqns =

dx = simplify(diff(eqns(1), t))

dx =

dy = simplify(diff(eqns(2), t))

dy =

dz = simplify(diff(eqns(3), t))

dz =

You could extend this to include rotations in Z or to include additional joints.

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Bruno Luong 2022-11-15

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编辑：Bruno Luong 2022-11-15

I guess you mistaken between

numerical finite difference https://fr.mathworks.com/help/matlab/ref/diff.html
and symbolic derivative https://fr.mathworks.com/help/symbolic/diff.html

Use the fist is just the difference of 3 rows of Q 3x3 matrix, there fore returns 2x3 matrix. It is NOT the derivative/