Symbolic Derivative in matlab

Can matlab diffrentiate F with respect to θ , ϕ and ψ only ?.

Any help is apperciated

Answer 1

[KSSV]

You can carry on symbolic calculations. Read about diff.

https://www.mathworks.com/help/symbolic/diff.html

[HN]

I've tried it but it differentiate variables that supposed to be assumed constant.

The following is the comman I used

V=simplify(diff(f,theta)+diff(f,psi)+diff(f,phi));

gives

EX, α is constant should not differentiated but the result is diffrent. So, I am confused if I make mistake or matlab cannot deal with this ?

Thank you KSSV

[KSSV]

Copy your code, which you have tried.

[HN]

syms phi theta psi  dphi dtheta dpsi  rp L alpha beta


x =   @(t) -rp*(cos(t)*cos(t)+sin(t)*sin(t)*sin(t))*cos(alpha)-rp*(-cos(t)*sin(t)+sin(t)*sin(t)*cos(t))*sin(alpha)+(rp/tan(alpha))*(cos(t)*sin(t)*(cos(alpha)-1)+cos(t)*cos(t)*sin(alpha));

dx=diff(x,theta)*dpsi+diff(x,psi)*dpsi+diff(x,psi)*dphi

It gives

dpsi*(rp*cos(alpha)*(cos(phi)*sin(theta) - cos(theta)*sin(phi)*sin(psi)) - rp*sin(alpha)*(sin(phi)*sin(theta) + cos(phi)*cos(theta)*sin(psi))) - dphi*((rp*sin(psi)*(sin(alpha + phi) - sin(phi)))/tan(alpha) + rp*cos(alpha)*cos(psi)*sin(phi)*sin(theta) + rp*cos(phi)*cos(psi)*sin(alpha)*sin(theta)) - dpsi*((rp*sin(psi)*(sin(alpha + phi) - sin(phi)))/tan(alpha) + rp*cos(alpha)*cos(psi)*sin(phi)*sin(theta) + rp*cos(phi)*cos(psi)*sin(alpha)*sin(theta))

But it is wrong

[KSSV]

syms t a x(t) y(t)
f = a*(cos(x)+sin(x)) ;
diff(f,t)

[HN]

Thank you KSSV ,

How about the symbolic division as below. matlab says undefined operator .

R =   -A*(cos(t)-cos(t))+B*cos(th)*sin(t);
S =    A*sin(t)*sin(t)-B*cos(t)+C*cos(t);
phi=atan(R/S)

[KSSV]

syms A B C t th 

R =   -A*(cos(t)-cos(t))+B*cos(th)*sin(t);
S =    A*sin(t)*sin(t)-B*cos(t)+C*cos(t);
phi=atan(R/S)

[HN]

Why running on live script and script gives different result for the same expression?

syms syms t phi(t) theta(t) psi(t)  dphi dtheta dpsi  rp L alpha beta

x=rp*sin(alpha)*(cos(theta)*sin(phi) - cos(phi)*sin(psi)*sin(theta)) - rp*cos(alpha)*(cos(phi)*cos(theta) + sin(phi)*sin(psi)*sin(theta)) + (rp*cos(psi)*(sin(alpha + phi) - sin(phi)))/tan(alpha)

diff(x, t)

using matlab mlx and matlab script. Both gives different result

mlx gives

vx=rp*cos(psi(t))*cos(theta(t))*sin(phi(t))*sin(alpha) - rp*cos(phi(t))*cos(psi(t))*cos(theta(t))*cos(alpha)

while running on matlab script gives

vx=((rp*cos(psi(t))*(cos(alpha + phi(t)) - cos(phi(t)))*diff(phi(t), t))/tan(alpha) - rp*sin(alpha)*(sin(phi(t))*sin(theta(t))*diff(theta(t), t) - cos(phi(t))*cos(theta(t))*diff(phi(t), t) + cos(phi(t))*cos(psi(t))*sin(theta(t))*diff(psi(t), t) + cos(phi(t))*cos(theta(t))*sin(psi(t))*diff(theta(t), t) - sin(phi(t))*sin(psi(t))*sin(theta(t))*diff(phi(t), t)) - rp*cos(alpha)*(cos(phi(t))*sin(psi(t))*sin(theta(t))*diff(phi(t), t) - cos(phi(t))*sin(theta(t))*diff(theta(t), t) - cos(theta(t))*sin(phi(t))*diff(phi(t), t) + cos(psi(t))*sin(phi(t))*sin(theta(t))*diff(psi(t), t) + cos(theta(t))*sin(phi(t))*sin(psi(t))*diff(theta(t), t)) - (rp*sin(psi(t))*(sin(alpha + phi(t)) - sin(phi(t)))*diff(psi(t), t))/tan(alpha))