Dot product does not work for symbolic vectors

Hi, I'm working on dynamics simulation with matlab, so I have the vector r with the size of [3 1]. I examine the calculation

dot(r,r) - (r(1)^2+r(2)^2 +r(3)^2) and I got an answer different than 0. Is there any explanation for this ?

syms t g real 
syms alpha1(t) beta1(t) gamma1(t) 
syms m1 m2 m3 m4 real 
syms h d1 d2 r1 r2 r3 r4 t1 t2 t3 L real 
syms a b c d5 real

r = [(a*b*c*d5*m1*sin(conj(gamma1(t))-gamma(t)))/(-a*b*c*m1 +pi*m3*r1^2*t1 +pi*m1*r1^2*t1);
      -(0.5000*(- a*b*c^2*m1 + a*b*c*m1*t1 + 3.1416*m3*r1^2*t1*t3 + 3.1416*m3*r1^2*t1^2))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1); 
      -(a*b*c*d5*m1*cos(conj(gamma1(t)) - gamma1(t)))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1) ]; 
r_x = r(1) ;
r_y = r(2) ;
r_z = r(3) ;
% dot minus sum of elements. This should be 0 
% I think this is a problem with dot function of MATLAB.
dot(r,r) - (r_x^2 + r_y^2 + r_z^2 )

ans = 

Answer 1

[Sam Chak]

Probably it has something to do with how MATLAB interprets 'gamma1(t)' .

syms t g y real 
syms alpha1(t) beta1(t) gamma1(t)
syms m1 m2 m3 m4 real 
syms h d1 d2 r1 r2 r3 r4 t1 t2 t3 L real 
syms a b c d5 real 

% r = [(a*b*c*d5*m1*sin(conj(gamma1(t)) - gamma1(t)))/(-a*b*c*m1 +pi*m3*r1^2*t1 +pi*m1*r1^2*t1);
%       -(0.5000*(- a*b*c^2*m1 + a*b*c*m1*t1 + 3.1416*m3*r1^2*t1*t3 + 3.1416*m3*r1^2*t1^2))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1); 
%       -(a*b*c*d5*m1*cos(conj(gamma1(t)) - gamma1(t)))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1) ]; 

r1  =  (a*b*c*d5*m1*sin(conj(y) - y))/(- a*b*c*m1 + pi*m3*r1^2*t1 + pi*m1*r1^2*t1);
r2  = -(0.5000*(- a*b*c^2*m1 + a*b*c*m1*t1 + pi*m3*r1^2*t1*t3 + pi*m3*r1^2*t1^2))/(- a*b*c*m1 + pi*m3*r1^2*t1 + pi*m1*r1^2*t1);
r3  = -(a*b*c*d5*m1*cos(conj(y) - y))/(- a*b*c*m1 + pi*m3*r1^2*t1 + pi*m1*r1^2*t1);

r   = [r1; 
       r2; 
       r3];

r_x = r(1);
r_y = r(2);
r_z = r(3);

% dot minus sum of elements. This should be 0 
% I think this is a problem with dot function of MATLAB.
A   = dot(r,r);
A   = simplify(A, 'steps', 100)

A = 

B   = (r_x)^2 + (r_y)^2 + (r_z)^2;
B   = simplify(B, 'steps', 100)

B = 

C   = A - B

C = 

0

Answer 2

[Torsten]

Since you cannot assume functions to be real-valued, you must use

dot(r,r) - (r_x*r_x' + r_y*r_y' + r_z*r_z' )

instead of

dot(r,r) - (r_x^2 + r_y^2 + r_z^2 )

[Dyuman Joshi]

Shouldn't it be 'have not' instead of 'can not' here?

[Torsten]

syms alpha1(t) beta1(t) gamma1(t) real

Warning: Can only make assumptions on variable names, not 'alpha1(t)'.

Warning: Can only make assumptions on variable names, not 'beta1(t)'.

Warning: Can only make assumptions on variable names, not 'gamma1(t)'.

Maybe there is a different way to tell MATLAB that the results of the functions will be real-valued, but I don't know how.

[Dyuman Joshi]

syms alpha1(t) beta1(t) gamma1(t)
assume(alpha1(t), 'real')
assumptions

ans = 

assumeAlso(beta1(t), 'real')
assumeAlso(gamma1(t), 'real')
assumptions

ans = 

conj(alpha1(t))

ans = 

[Torsten]

syms t g real 
syms alpha1(t) beta1(t) gamma1(t) 
syms m1 m2 m3 m4 real 
syms h d1 d2 r1 r2 r3 r4 t1 t2 t3 L real 
syms a b c d5 real
assume(alpha1(t), 'real')
assumeAlso(beta1(t), 'real')
assumeAlso(gamma1(t), 'real')
r = [(a*b*c*d5*m1*sin(conj(gamma1(t))-gamma(t)))/(-a*b*c*m1 +pi*m3*r1^2*t1 +pi*m1*r1^2*t1);
      -(0.5000*(- a*b*c^2*m1 + a*b*c*m1*t1 + 3.1416*m3*r1^2*t1*t3 + 3.1416*m3*r1^2*t1^2))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1); 
      -(a*b*c*d5*m1*cos(conj(gamma1(t)) - gamma1(t)))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1) ]; 
r_x = r(1) ;
r_y = r(2) ;
r_z = r(3) ;
% dot minus sum of elements. This should be 0 
% I think this is a problem with dot function of MATLAB.
dot(r,r) - (r_x^2 + r_y^2 + r_z^2 )

ans = 

[Dyuman Joshi]

There might be a typo in the code and it should be gamma1(t) instead of gamma(t), as is the case in the cos term in 3rd row -

syms t g real 
syms alpha1(t) beta1(t) gamma1(t) 
syms m1 m2 m3 m4 real 
syms h d1 d2 r1 r2 r3 r4 t1 t2 t3 L real 
syms a b c d5 real
assume(alpha1(t), 'real')
assumeAlso(beta1(t), 'real')
assumeAlso(gamma1(t), 'real')

%%                                         v 
r = [(a*b*c*d5*m1*sin(conj(gamma1(t))-gamma1(t)))/(-a*b*c*m1 +pi*m3*r1^2*t1 +pi*m1*r1^2*t1);
      -(0.5000*(- a*b*c^2*m1 + a*b*c*m1*t1 + 3.1416*m3*r1^2*t1*t3 + 3.1416*m3*r1^2*t1^2))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1); 
      -(a*b*c*d5*m1*cos(conj(gamma1(t)) - gamma1(t)))/(- a*b*c*m1 + 3.1416*m3*r1^2*t1 + 3.1416*m1*r1^2*t1) ]; 
r_x = r(1) ;
r_y = r(2) ;
r_z = r(3) ;

dot(r,r) - (r_x^2 + r_y^2 + r_z^2 )

ans = 

0