How to derive an angle to time in mupad

Question

So I have a pritty nasty function with sines and cosines that represents the position of some point in a certain system. Now that I know the location of the point dependant on angle Beta. I wish to derive the function to find the speed. The problem is that mupad thinks that beta is a constant when you try to derive it to time. Obiously the derivative of Beta is the angular velocity. But how do I tell this to mupad?

This is the code I have so far.

reset();
eq:=(a/cos(Beta))^2=(a/cos(Alpha))^2+d^2-2*a/cos(Alpha)*d*sin(Alpha);

Ex:=-a+Lb*cos(Beta);

a:=simplify(solve(eq,a,Real,IgnoreAnalyticConstraints) assuming PI/2<Alpha<PI and 0<Beta<PI/2)[2][1]

Ex:=((combine(Ex,IgnoreAnalyticConstraints)) assuming Beta in R_ and 0<Beta<PI/2)

plot(Ex|[d=0.122,Alpha=11.5*PI/180,Lb=0.8],Beta=0..PI/2,Scaling=Constrained);

Ey:=a*tan(Alpha)+Lb*sin(Beta)

plot(Ey|[d=0.122,Alpha=11.5*PI/180,Lb=0.8],Beta=0..PI/2,Scaling=Constrained)

d:=0.09:
Alpha:=11.5*PI/180:
Lb:=0.85:

plot1:=plot::Curve2d([Ex,Ey],Beta=0..PI/2):
plot2:=plot::Point2d([Ex,Ey],Beta=0..PI/2,Frames=200):
plot(plot1,plot2,x=0.65,ViewingBoxXRange=0..0.7, ViewingBoxYRange=0..0.9, Scaling=Constrained);
delete(d);delete(Alpha);delete(Lb);


pointE:=matrix([Ex,Ey])

diff(pointE,t) assuming diff(Beta,t)=Omega

I tried something in the last line but it clearly didn't work.

Answer 1

I found the solution to this problem:

V_E:=diff(puntE|[Beta=Beta(t)],t)