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C_R

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How to apply initial conditions to a fle...

C_R 2582 MapleSim
beam
May 09 2023
0 0

I was not able to apply ICs (initial conditions) using the advanced parameter settings of the flexible beam component in the attached file. My intention is to have a beam moving at t=0s (velocity of end frame <> 0). The computed initial values for the elastic coordinates (see output console for the disabled component below encircled in red) indicate that the flexible beam has no kinetic energy at t=0s.

A workaround is to attach a rigid body to the end frame and apply the ICs to the body. (Inertia and mass of the rigid body can be set to zero.)

How to apply initial conditions to the disabled component so that it moves as the workaround?

Imposing_IC_v.msim

How get all solutions of this "periodic"...

C_R 2582 Maple
rootfinding numeric rootof
April 30 2023
2 2

Ideally, I would like to find all roots of this RootOf expression for a given interval.

I tried defining a function from the argument of the RootOf expression and using fsolve to find solutions, but could not get all of them.

What I managed to do skips the interval, is not really elegant and raises additional questions.
I would be grateful for any hints and improvements.

RootOf(_Z*cos(_Z)-sqrt(sin(_Z)^2))

RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))

 (1)

allvalues(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2)))

Error, (in RootOf/sort1) cannot numerically evaluate the argument

  

RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), index = i)

RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2), index = i)

 (2)

evalf(subs(i = 3, RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2), index = i)))

RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2), index = 3)

 (3)

evalf(RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 3))

-4.493409458

 (4)

rt := ''RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), i)''

'RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), i)'

 (5)

subs(i = 3, rt)

RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 3)

 (6)

evalf(RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 3))

-4.493409458

 (7)

seq(subs(i = k, rt), k = 1 .. 5)

RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 1), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 2), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 3), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 4), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 5)

 (8)

evalf(%)

0., 0., -4.493409458, 4.913180439, 4.913180439

 (9)

{-4.493409458, 0., 4.913180439}[]

-4.493409458, 0., 4.913180439

 (10)

seq(evalf(subs(i = k, rt)), k = 1 .. 5)

Error, (in evalf/RootOf) numeric exception: division by zero

  

evalf(seq(subs(i = k, rt), k = 1 .. 5))

Error, (in evalf/RootOf) numeric exception: division by zero

  

NULL

seq(subs(i = k, rt), k = -5 .. 5)

RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), -5), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), -4), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), -3), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), -2), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), -1), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 0), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 1), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 2), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 3), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 4), RootOf(op(RootOf(_Z*cos(_Z)-(sin(_Z)^2)^(1/2))), 5)

 (11)

evalf(%)

-4.493409458, -4.493409458, -2.028757845, -2.028757838, 4.913180439, 0., 0., 0., -4.493409458, 4.913180439, 4.913180439

 (12)

NULL

NULL

Download RootOf_a_periodic_function.mw

Can some suppress (i.e. ignore) the warn...

C_R 2582 MapleSim 2023
warning
April 27 2023
1 1

I cannot. If I right click on the warning I get only a copy option

Double_Pendulum_warning.msim

Is this an endpoint of function composit...

C_R 2582 Maple
functional-operator
April 25 2023
1 1

Example

diff(w(x), x, x) = F*((6*(-a^2/(2*L^2)+a^3/(3*L^3)))*x+2*a^2/L-a^3/L^2)/EI

diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI

 (1)

Eval(lhs(diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI), x = L) = (`@`(simplify, eval))(rhs(diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI), x = L)

Eval(diff(diff(w(x), x), x), x = L) = -F*a^2*(L-a)/(L^2*EI)

 (2)

Can the expression above be further shortened by function composition and function application (to a single group of arguments)? I tried

(`@`(Eval, lhs) = `@`(`@`(simplify, eval), rhs))(diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI, x = L)

Error, (in evalapply) invalid input: lhs expects 1 argument, but received 2

  

which does not work.
Since the error message is clear I am looking for a single argument command that could replace lhs and rhs.  

Analog to evalf, which accepts an index, I tried to replace lhs by

op[1](diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI)

diff(diff(w(x), x), x), F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI

 (3)

to do the same as

op(1, diff(diff(w(x), x), x) = F*(6*(-(1/2)*a^2/L^2+(1/3)*a^3/L^3)*x+2*a^2/L-a^3/L^2)/EI)

diff(diff(w(x), x), x)

 (4)

Unfortuenatly this does not work. Are there any other options or have I reached an end point?

Would a single argument variant of op make sense for other purposes than the example above?


Download replacement_of_lhs_and_rhs_by_single_argument_function.mw

Would it make sense to add a second hint...

C_R 2582 MaplePrimes
attachment
April 14 2023
0 2

Often, in response to a question without code, the suggestion is made to upload a Maple file using the button with the green arrow .

This happens so often that I get the impression that new users don't recognize this as the best and most efficient way to get their question analyzed and answered. Or they just don't know how to do it.

So why not adding a hint to consider uploading code just before "Suggested Tags"?

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