Hi,
I am deriving second order differential equation in MATLAB. I have defined a time dependent variable and then applied some derivative operations like below.
syms a b;
th = sym('th(t)');
y = diff(a^2*cos(th)+(b/12)*sin(th));
thd = diff(th);
ybythd = diff(y,thd);
p = diff(ybythd);
These operations calculates the value of p as following-
p = diff(diff((b*cos(th(t))*diff(th(t), t))/12 - a^2*sin(th(t))*diff(th(t), t), t), diff(th(t), t))
Now, I want to plot the variable p wrt time t. Before plotting, I substituted the value of symbols a and b
newP = subs(p,[a,b],[2.1,9.5])
newP = diff((19*cos(th(t))*diff(th(t), t, t))/24 - (19*sin(th(t))*diff(th(t), t)^2)/24 - (441*cos(th(t))*diff(th(t), t)^2)/100 - (441*sin(th(t))*diff(th(t), t, t))/100, diff(th(t), t))
The variable th = sin(2*pi*t); should be substituted in order to convert the above second order differential equation into a liner equation of time t. Later on the following commands can plot p wrt time t -
syms t
thAct = sin(2*pi*t);
time = 0.0:0.1:5.0;
for i = 1:length(time)
temp = subs(newP,th,thAct);
pVal(i)= subs(temp,t,time(i));
end
plot(time,pVal);
But the above code does not work. Somebody please tell me how to substitute the parameters in second order differential equation.
-
Thanks
Ravi
