Converting from symbolic to numerical data

I tried using double to convert from symbolic to numerical data but it is giving me the wrong answer.

syms A B C D theta(t) omega1(t) alpha1(t) t
assume([A B C D],"real")

Displacement analysis

syms beta(t) phi(t) 
%for equilibrium, sum of displacement component on x and y axis must
%respectively be equal to zero
xdisp = A*cos(theta) + B*cos(beta) - C*cos(phi) - D == 0;
ydisp = A*sin(theta) + B*sin(beta) - C*sin(phi) == 0;
[angB,angD] = solve([xdisp,ydisp],[beta(t),phi(t)])

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

angB = 

angD = 

angB = simplify(angB);
angD = simplify(angD);

Velocity analysis

xvel = diff(xdisp,t);
yvel = diff(ydisp,t);
syms omega2(t) omega3(t)
xvel = subs(xvel,[diff(beta(t), t),diff(phi(t), t),diff(theta(t), t)],[omega2(t),omega3(t),omega1(t)]);
yvel = subs(yvel,[diff(beta(t), t),diff(phi(t), t),diff(theta(t), t)],[omega2(t),omega3(t),omega1(t)]);
[velB,velD] = solve([xvel,yvel],[omega2(t),omega3(t)]);
velB = simplify(velB);
velD = simplify(velD);

Acceleration analysis

xacc = diff(xvel,t);
yacc= diff(yvel,t);
syms alpha2(t) alpha3(t)
xacc = subs(xacc,[diff(omega1(t),t),diff(omega2(t),t),diff(omega3(t),t),diff(beta(t),t),diff(phi(t),t),diff(theta(t),t)],[alpha1(t),alpha2(t),alpha3(t),omega2(t),omega3(t),omega1(t)]);
yacc = subs(yacc,[diff(omega1(t),t),diff(omega2(t),t),diff(omega3(t),t),diff(beta(t),t),diff(phi(t),t),diff(theta(t),t)],[alpha1(t),alpha2(t),alpha3(t),omega2(t),omega3(t),omega1(t)]);

[accB,accD] = solve([xacc,yacc],[alpha2(t),alpha3(t)]);
accB = simplify(accB);
accD = simplify(accD);

Numerical values of the displacement, velocity and acceleration

angB = subs(angB,[A B C D theta(t) omega1(t) alpha1(t)],[300 360 360 600 30 10 -30]);
angD = subs(angD,[A B C D theta(t) omega1(t) alpha1(t)],[300 360 360 600 30 10 -30]);
angB = simplify(angB)

angB = 

angD = simplify(angD)

angD = 

angulardisp1 = double(angB)

angulardisp1 = 2×1

1.0024 -0.0194

If i use calculator to check th answer of angB it gives 35.12 which is correct but if i use double to convert the symbolic data to numerical data it gives 1.0024 which is wrong.

Answer 1

[John D'Errico]

Do you understand that sin and cos assume RADIANS, NOT degrees? But you are substituting in angles that are clearly in terms of DEGREES.

angB = subs(angB,[A B C D theta(t) omega1(t) alpha1(t)],[300 360 360 600 30 10 -30]);

There is a difference, and it is important.

help sin

 SIN    Sine of argument in radians.
    SIN(X) is the sine of the elements of X.
 
    See also ASIN, SIND, SINPI.

    Documentation for sin
       doc sin

    Other uses of sin

       codistributed/sin    fixedpoint/sin    sym/sin         tabular/sin
       dlarray/sin          gpuArray/sin      symbolic/sin

MATLAB cannot know that you think of angles in terms of degrees, since it cannot read your mind. Even after all these years, the mindreading toolbox is still in the debugging phase.

You can convert degrees to radians by multiplying by pi/180, or you can use the deg2rad function to do it for you. For example, 30 degrees is pi/6 radians.

[Cris LaPierre]

To add on to this answer, either substitute radian degress, or use cosd and sind to define xdisp and ydisp.

syms A B C D theta(t) omega1(t) alpha1(t) t
assume([A B C D],"real")

syms beta(t) phi(t) 
%for equilibrium, sum of displacement component on x and y axis must
%respectively be equal to zero
xdisp = A*cosd(theta) + B*cosd(beta) - C*cosd(phi) - D == 0;
ydisp = A*sind(theta) + B*sind(beta) - C*sind(phi) == 0;
[angB,angD] = solve([xdisp,ydisp],[beta(t),phi(t)]);

Warning: Solutions are only valid under certain conditions. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.

angB = simplify(angB);
angD = simplify(angD);

xvel = diff(xdisp,t);
yvel = diff(ydisp,t);
syms omega2(t) omega3(t)
xvel = subs(xvel,[diff(beta(t), t),diff(phi(t), t),diff(theta(t), t)],[omega2(t),omega3(t),omega1(t)]);
yvel = subs(yvel,[diff(beta(t), t),diff(phi(t), t),diff(theta(t), t)],[omega2(t),omega3(t),omega1(t)]);
[velB,velD] = solve([xvel,yvel],[omega2(t),omega3(t)]);
velB = simplify(velB);
velD = simplify(velD);

xacc = diff(xvel,t);
yacc= diff(yvel,t);
syms alpha2(t) alpha3(t)
xacc = subs(xacc,[diff(omega1(t),t),diff(omega2(t),t),diff(omega3(t),t),diff(beta(t),t),diff(phi(t),t),diff(theta(t),t)],[alpha1(t),alpha2(t),alpha3(t),omega2(t),omega3(t),omega1(t)]);
yacc = subs(yacc,[diff(omega1(t),t),diff(omega2(t),t),diff(omega3(t),t),diff(beta(t),t),diff(phi(t),t),diff(theta(t),t)],[alpha1(t),alpha2(t),alpha3(t),omega2(t),omega3(t),omega1(t)]);

[accB,accD] = solve([xacc,yacc],[alpha2(t),alpha3(t)]);
accB = simplify(accB);
accD = simplify(accD);

angB = subs(angB,[A B C D theta(t) omega1(t) alpha1(t)],[300 360 360 600 30 10 -30]);
angD = subs(angD,[A B C D theta(t) omega1(t) alpha1(t)],[300 360 360 600 30 10 -30]);
angB = simplify(angB);
angD = simplify(angD)

angD = 

angulardisp1 = double(angB)

angulardisp1 = 2×1

35.1162 -82.7042