@Rouben Rostamian  

Hello Rouben,

First of all thank you a lot for the help and the mw file you provided!  That helped me a LOT.

Now I have another thing I am trying to do, and it seems not readily possible.  I have an expression like this:

T1 := (-m*omega(t)^2*r(t)+k*r(t))^2+r(t)^2*omega(t)^2*c^2 = omega(t)^4*m^2*u^2

I want to "extract" or "isolate" a term composed of two terms, in my case "r(t)/u" which is in vibration applications, the transmissibility (output / input).

I tried with isolate, solve, and many other functions, not working.  Best I could do is a solve which of course is not mathematically correct.  Can Maple rearrange terms to extract a ratio out of an expression?

By hand this is easy, so I would imagine Maple can easily do it.  I would expect to exactly obtain this:

r(t)/u = m*omega^2/sqrt([(-m*omega^2+k)^2+c*omega^2])

BTW when I use isolate to solve for a term, I get "RootOf" with "_Z" constants.  Is that normal?  Maple seems to be solving the roots of the function in respect to the term and the Z constants seems to be for numeric constants but why Maple is adding numeric constants without numeric evaluation??  Doing a isolate(T1,r(t)) gives:

r(t) = RootOf((omega(t)^4*m^2+omega(t)^2*c^2-2*omega(t)^2*k*m+k^2)*_Z^2-omega(t)^4*m^2*u^2)

As usual, thank you and best regards!

@Rouben Rostamian  

Hello Rouben.  OK thanks for the additional advice, using tilde worked for the differential of vectors and simplified my worksheet greatly!

I am however trying to substitute some variables to zero since they are differentials of constants.  For example in my application Omega(dot) is the angular acceleration and since angular velocity is constant, it will be equal to zero.  So from the following vector system:

F_D := (Vector(3, {(1) = m*(diff(r(t), t, t)-(diff(phi(t), t))^2*r(t)-cos(beta(t))*u*omega(t)^2-sin(beta(t))*u*(diff(omega(t), t))), (2) = m*((diff(phi(t), t, t))*r(t)+2*(diff(phi(t), t))*(diff(r(t), t))-sin(beta(t))*u*omega(t)^2+cos(beta(t))*u*(diff(omega(t), t))), (3) = 0})) = (Vector(3, {(1) = -c*(diff(r(t), t))-k*r(t), (2) = -r(t)*(diff(phi(t), t))*c, (3) = 0}))

I have created the following subs:

rel3s := diff(omega(t), t) = 0; rel4s := diff(phi(t), t) = omega(t); rel5s := diff(phi(t), t, t) = 0

Then substituted with

ED := simplify(F_D, {rel3s, rel4s, rel5s})

But I get

ED := (Vector(3, {(1) = (-cos(beta(t))*m*u-r(t)*m)*(diff(phi(t), t))^2+m*(diff(r(t), t, t)), (2) = -sin(beta(t))*m*u*(diff(phi(t), t))^2+2*m*(diff(phi(t), t))*(diff(r(t), t)), (3) = 0})) = (Vector(3, {(1) = -c*(diff(r(t), t))-k*r(t), (2) = -r(t)*(diff(phi(t), t))*c, (3) = 0}))

As you can see, Phi(dot) is not being replaced by Omega as required by expression rel4s...

I tried inverting the declaration of the expressions (omega(t) = diff(phi(t), t)) but the same happens.

Finally, how do you reorganize an expression to "send" a variable and its derivatives to a specific side of the expression?  For example, I'd like r, r(dot) and r(dot)(dot) to be on the left hand side of the equation so it becomes a simple second order differential equation??

After that I think I will have completed my first maple tutorial!!

Best regards

@Rouben Rostamian  

Ok here it is!  You will see there may be several things I should have done differently.  For example differentiating vectors.  Right now I differentiate each component of a vector by using diff(Vector[i,j,k],t) but I'd like to be able to differentiate the entire vector in one command.

Anyways let me know what you find!  Thanks again!

Script.mw

@Rouben Rostamian

Hey thanks for the hints!  I really need to do some tutorials as this seemed pretty basic ;)

I managed to get past the assignments, and now this works.  However, Maple is still not simplifying my vector using rels1 & rels2.

Any idea?