How to substitute a value for the time derivative of a function

Hellow

I have a dispalcemet function of time defined as:

syms d(t)

>> a = d^2+sin(d)

The first derivative is the velocity:

>> v = diff(a)

v(t) =

cos(d(t))*diff(d(t), t) + 2*d(t)*diff(d(t), t)

the parameter diff(d(t), t) means the velocity value but How I can substitute a value for it using subs or any other function?

thank you

Answer 1

[madhan ravi]

use subs() like below:

syms d(t)
a = d^2+sin(d);
v = diff(a);
after=subs(v,diff(d),2)  % here diff(d) is replace number 2

Gives:

after(t) =
 
2*cos(d(t)) + 4*d(t)

or use ode45() -> diff(d,2)==>acceleration the right hand side is as it is so we treat them now as second order ode which is then further reduced to first order odes.

[t,x]=ode45(@myod2,[0 2],[0;1]);
figure(1)
plot(t,x(:,1),'-ok')
figure(2)
plot(t,x(:,2),'-or')
function dxdt = myod2(t,Y) 
dxdt=[Y(2);
 sin(Y(1)) + Y(1)^2];
end

[Hazim Nasir]

thank you for reply

Acually this equation is just an example, I have appllied subs to my function and get to long sentence like that:

(40911*sin(30)^2*sin(40)^2)/25000 - (151893819*cos(120)^2*sin(40))/25000000.................

I don't know why not MATLAB just return a single final value

[madhan ravi]

just use vpa() to get a number

[Hazim Nasir]

MANY THANKS

[madhan ravi]

Anytime :)