MaplePrimes Questions

I am trying to model a parallel manipulator but I am receiving an error message

State variable'diff(diff(`Main.R41.theta`(t),t),t)' does not appear in dynamic or constraint equations.

I tried changing the Revolute joint 41 but the same error is repeated. 

You can find my model here: ParalelManipulator_v2.msim

Can you help me solve this issue? Thank you in advance!

Dear All,

I wanted to check the calcultations carried out in a Journal Article I was reading as I was not very convinced.

The objective is to find q1i, q2i, q3i in terms of px, py, and pz and constant parameters φ, a, b, h, and r.

I have realised that the results given by the article do not match with the solution to the dsolve command.

Could you please spot where the mistake is?

My Solution: IK_equations.mw

help me on thispde_solutionalpha.mw
 

restart

M := 1; S := .78; K := .5; Sh := .2; alpha := .7; R := .3; N := .6; k := .5

pde1 := diff(u(y, t), t)+S.(diff(u(y, t), y))-2*k^2*u(y, t) = diff(u(y, t), y, y)+theta(y, t)+N.C(y, t)+M.u(y, t)+u(y, t)/K

                pde2 := theta(y, t)+t*(diff(theta(y, t), t))+S*(diff(theta(y, t), y)) = (diff(theta(y, t), y, y))/Pr-alpha.theta(y, t)

pde3 := C(y, t)+t*(diff(C(y, t), t))+S*(diff(C(y, t), y)) = (diff(C(y, t), y, y))/Sh-R.C(y, t)

PDE := unapply({pde || (1 .. 3)}, Pr)

proc (Pr) options operator, arrow; {C(y, t)+t*(diff(C(y, t), t))+.78*(diff(C(y, t), y)) = 5.000000000*(diff(diff(C(y, t), y), y))-.3*C(y, t), diff(u(y, t), t)+.78*(diff(u(y, t), y))-.50*u(y, t) = diff(diff(u(y, t), y), y)+theta(y, t)+.6*C(y, t)+3.000000000*u(y, t), theta(y, t)+t*(diff(theta(y, t), t))+.78*(diff(theta(y, t), y)) = (diff(diff(theta(y, t), y), y))/Pr-.7*theta(y, t)} end proc

(1)

IBC := {C(0, t) = 1, C(1, t) = 0, C(y, 0) = 0, theta(0, t) = 1, theta(1, t) = 0, theta(y, 0) = 0, u(0, t) = 0, u(1, t) = 0, u(y, 0) = 0}

``

PrList := [.71, 7, 10, 100]; Colours := table(`~`[`=`](PrList, ["blue", "red", "green", "cyan"])); for Pr in PrList do pds := pdsolve(PDE(Pr), IBC, numeric); Plots[Pr] := pds:-plot[display](u(y, t), t = .5, linestyle = "solid", colour = Colours[Pr], legend = sprintf("Pr=%2.2f", Pr), title = "Velocity Profile", labels = ["y", "theta"]) end do; plots:-display([seq(Plots[Pr], `in`(Pr, PrList))])

 

NULL


 

Download pde_solutionalpha.mw

 

Dear All,

I'm stuck in a question, perhaps somebody can help. I have to solve the following equation: 

restart;
with(LinearAlgebra);
A := Matrix(3, 3, [[1, 3, 2], [4, 5, 1], [3, 7, 2]]);
      
M := IdentityMatrix(3);
   
eq := A^2*a+A*b+M*c;
K:= A^-2
Set := {seq(eq[i] = K[i], i = 1 .. nops(eq))};

 

But now I want to solve for a, b and c. I tried this with the solve function, but I gives an error. What do I have to do now?

Math


                            

 

Hello,

I'm trying to find the way to manipulate matrix equalities easily and isolate them as variables like if they were simple real variables but keeping the matrix properties.  However, I couldn't find the way to do it efficiently without describing all the parameters of the matrices.  I'd like to keep them as variables rather than perform matrix operations when defining the expressions. I've attached a snapshot which describes my problem much better:pdf_kmaple.pdf.

For instance, I'd like to be able to isolate the expression that defines the state-space when I change the discretization method.  

I'm wondering if there's a generic way I can use to isolate other matrix systems as well.

Thank you very much for your help!

JMarc

fgh := proc (x) options operator, arrow; [x, x^2, x^3] end proc;

sol := proc (x) options operator, arrow; min(`~`[Re](select(proc (t) options operator, arrow; is(abs(Im(t)) < 0.1e-19) and is(0 < Re(t)) end proc, fgh(x)))) end proc;

eval('sol(x)', [x = X]);

eval(%, X = 1)

 

Why does this not work?

Good morning,

I've been having some trouble entering this expression in Maple 17.

My teacher suggested using this format, however, this format is from 2004 and certainly isn't recognized by the current version of Maple, as it keeps spitting back 0=0 no matter how many different ways I try to enter it.

Could anyone provide feedback on the correct syntax of how to enter this expression? Thank you very much for your time.

Exporting one plot in program works well:

       MapleEngine.EvalMapleStatement(kv, "Export(\"D:\\\\MyGraph.jpeg\",plot(sin(x)*cos(2*x)));");

But if I'm trying to export two plots, program stops working and prints no exception:
        MapleEngine.EvalMapleStatement(kv, "Export(\"D:\\\\MyGraph.jpeg\",plot(sin(x)*cos(2*x)));");
        MapleEngine.EvalMapleStatement(kv, "Export(\"D:\\\\MyGraph2.jpeg\",plot(sin(x)*cos(2*x)));");

What is the cause?

Hello,

I work in maple  2017,but the "interface "command seems doesn't work. But it works in the old version(maple 18). Does anyone know what problem with it?

restart; with(PDEtools);
U := diff_table(Psi(`&psi;_2`, `&psi;_1`));
pde := `&psi;_2`*(diff(Psi(`&psi;_2`, `&psi;_1`), `&psi;_1`))+`&psi;_1`*U[`&psi;_1`]+2*U[] = 0;
&psi;_2 Psi(&psi;_2 + 1, &psi;_1)

   + &psi;_1 Psi(&psi;_2 + 1, &psi;_1) + 2 Psi(&psi;_2, &psi;_1) = 

  0
pdsolve(pde);
Error, (in pdsolve/info) first argument is not a differential equation

How can i solve it?

My Maple worksheet is attached below - where I am solving two quantum mechanics problems, trying to find the eigenvalues for certain potentials.  Using a previous post in Mapleprime (https://www.mapleprimes.com/questions/221629-Can-Maple-Find-Solution-To-Eigenvalue),  I saw how to get the lowest eigenvalue.  My question is how using numeric solutions, I can get the higher eigenvalues and corresponding solutions.  Is there a way to specify that e (the eigenvalue) has to be in a certain range.  I tried to specify assumptions (e>0.6), but that didn't work.  I know that for the second problem (using the shooting method) that the 4 lowest eigenvalues are 0.184358, 0.70747, 1.2065, 1.5625.  Thank you very much for you consideration.

 

ODE_BVP_eigenvalues.mw

 

 

Why does solve not find the value of xp = sqrt(1-v^2) in this worksheet?

SpecialRelativity.mw

Reference: Special Relativity and Classical Field Theory. Authors: Leonard Susskind and Art Friedman

I think I've seen this somewhere in Mapleprimes but I can't locate it. How do you pull the type and number of operations from an equation? 

a:=3*x^3-5*x^2+3*y

                   " *,^,-,*,^,+,* "

 

f := (s) -> -HankelH1(1, s)-2*I/Pi*BesselK(1, s);

evalf(Int(f(s), s = 0 .. 1));
                 -0.2348023134 + 0.3562894462 I

evalf(Int(Re(f(1.*s)), s = 0 .. 1)+I*Int(Im(f(1.*s)), s = 0 .. 1));
                 -0.2348023134 + 0.3562894462 I

evalf(Int(f(1.*s), s = 0 .. 1));
               -0.2094198744 + Float(infinity) I

I don't know if the third one is really an issue, but given that the first two work fine, looks suspicious.

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