Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer


 

restart; with(VectorCalculus)

r := `<,>`(sin(t), cos(t), t)

Vector(3, {(1) = 0.2739493386e-115+0.2739493386e-115*I, (2) = 1.0-0.7504824014e-231*I, (3) = t})

(1)

``


what??

Download problem.mw

How I can take Laplace Transform from equation.

Thanks

LAPLACE

The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

EllipseRoll.mw

i have a diff equation(in photo last one)ehich code coulde solve it?

 

Earlier smoothly working generation of normal distribution in v. 2019 unexpectedly shows the error:

RandV  := Statistics[RandomVariable](Normal(0, 1));
Statistics[Sample](RandV, 10);

Error, (in p) unable to convert Float(undefined) to an integer

 

Help create file Excel in ExcelTools, but error row 564?

thu_file.mw

Please help me? 

Hii,

I am using a command -NLPSolve(Ecost1, Q = 10 .. 20, initialpoint = {Q = 10}, assume = nonnegative, maximize = false). I am looking for solution that find the Q value at the minimum value of Ecost1. But Ecost1 should not go below 0. 

and also I am getting an error -Warning, initialpoint option ignored by solver.

Kindly tell how to deal with these issues.

 

Thanks

How I can do ?

Thank you.

 

Substitution of . 5,6,7) into Eqs. 1–(4), gives the new equation as functions of the generalized coordinates,
u_m,n(t);  v_m,n ( t), and w_m,n ( t). These expressions are then inserted in the Lagrange equations (see Eq. 8)) a set of N second-order coupled ordinary differential equations with both quadratic   and cubic nonlinearities.

In Eq (8) q are generalized coordinate such as uvw  and q = {`u__m,n`(t), `v__m,n`(t), `w__m,n`(t)}^T.

\where the elements of the vector,q_i are the time-dependent generalized coordinates.

L_Maple
 

U = (1/2)*(int(int(int(E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x))+v(x, y, t)*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y))))*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x)))/(-nu^2+1)+E*(`&PartialD;`(nu(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y))+v(x, y, t)*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(x))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x))-z*(diff(w(x, y, t), x, x))))*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))^2+`&PartialD;`(w(x, y, t))/`&PartialD;`(y)*(`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y))-z*(diff(w(x, y, t), y, y)))/(-nu^2+1)+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(y)+`&PartialD;`(v(x, y, t))/`&PartialD;`(x)+`&PartialD;`(w(x, y, t))/`&PartialD;`(x)*(`&PartialD;`(w(x, y, t))/`&PartialD;`(y))+`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y))+`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y))-2*z*(diff(w(x, y, t), x, y)))^2/(2*(1+nu))+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), x, y))^2/(1+nu)+E*l^2*(diff(w(x, y, t), y, y)-(diff(w(x, y, t), x, x)))^2/(2*(1+nu))+E*l^2*(diff(v(x, y, t), y, y)-(diff(u(x, y, t), x, x)))^2/(8*(1+nu))+E*l^2*(diff(v(x, y, t), x, y)-(diff(u(x, y, t), y, y)))^2/(8*(1+nu)), z = -(1/2)*h .. (1/2)*h), y = 0 .. b), x = 0 .. a))

U = (1/2)*(int(int((1/12)*(-E*(-v(x, y, t)*(diff(diff(w(x, y, t), y), y))-(diff(diff(w(x, y, t), x), x)))*(diff(diff(w(x, y, t), x), x))/(-nu^2+1)-E*(-v(x, y, t)*(diff(diff(w(x, y, t), x), x))-(diff(diff(w(x, y, t), y), y)))*(diff(diff(w(x, y, t), y), y))/(-nu^2+1)+4*E*(diff(diff(w(x, y, t), x), y))^2/(2+2*nu))*h^3+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2+v(x, y, t)*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2))*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2)*h/(-nu^2+1)+E*(`&PartialD;`(nu(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2+v(x, y, t)*(`&PartialD;`(u(x, y, t))/`&PartialD;`(x)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(x)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(x)^2))*(`&PartialD;`(v(x, y, t))/`&PartialD;`(y)+(1/2)*`&PartialD;`(w(x, y, t))^2/`&PartialD;`(y)^2+`&PartialD;`(w(x, y, t))*`&PartialD;`(w__0(x, y, t))/`&PartialD;`(y)^2)*h/(-nu^2+1)+E*(`&PartialD;`(u(x, y, t))/`&PartialD;`(y)+`&PartialD;`(v(x, y, t))/`&PartialD;`(x)+`&PartialD;`(w(x, y, t))^2/(`&PartialD;`(x)*`&PartialD;`(y))+2*`&PartialD;`(w__0(x, y, t))*`&PartialD;`(w(x, y, t))/(`&PartialD;`(x)*`&PartialD;`(y)))^2*h/(2+2*nu)+2*E*l^2*(diff(diff(w(x, y, t), x), y))^2*h/(1+nu)+E*l^2*(diff(diff(w(x, y, t), y), y)-(diff(diff(w(x, y, t), x), x)))^2*h/(2+2*nu)+E*l^2*(diff(diff(v(x, y, t), y), y)-(diff(diff(u(x, y, t), x), x)))^2*h/(8+8*nu)+E*l^2*(diff(diff(v(x, y, t), x), y)-(diff(diff(u(x, y, t), y), y)))^2*h/(8+8*nu), y = 0 .. b), x = 0 .. a))

(1)

T = rho*h*(int(int((`&PartialD;`(u(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(v(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(w(x, y, t))/`&PartialD;`(t))^2, y = 0 .. b), x = 0 .. a))

T = rho*h*(int(int(`&PartialD;`(u(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(v(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(w(x, y, t))^2/`&PartialD;`(t)^2, y = 0 .. b), x = 0 .. a))

(2)

F = (1/2)*c*(int(int((`&PartialD;`(u(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(v(x, y, t))/`&PartialD;`(t))^2+(`&PartialD;`(w(x, y, t))/`&PartialD;`(t))^2, y = 0 .. b), x = 0 .. a))

F = (1/2)*c*(int(int(`&PartialD;`(u(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(v(x, y, t))^2/`&PartialD;`(t)^2+`&PartialD;`(w(x, y, t))^2/`&PartialD;`(t)^2, y = 0 .. b), x = 0 .. a))

(3)

W = int(int(w(x, y, t)*f__1(x, y, t)*cos(omega*t), y = 0 .. b), x = 0 .. a)

W = int(int(w(x, y, z)*f__1(x, y, z)*cos(omega*t), y = 0 .. b), x = 0 .. a)

(4)

u(x, y, t) = sum(sum(`u__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

u(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`u__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(5)

v(x, y, t) = sum(sum(`v__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

v(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`v__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(6)

w(x, y, t) = sum(sum(`w__m,n`(t)*sin(m*Pi*x/a)*sin(n*Pi*y/b), n = 1 .. N), m = 1 .. M)

w(x, y, t) = -(1/4)*(cos(Pi*y*N/b)*cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*y*N/b)*cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y/b)+cos(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)-cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)*cos(Pi*y/b)-cos(Pi*y*N/b)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)-cos(Pi*x/a)*sin(Pi*y/b)*sin((M+1)*Pi*x/a)+cos((M+1)*Pi*x/a)*sin(Pi*x/a)*sin(Pi*y*N/b)+sin(Pi*x/a)*sin(Pi*y/b)*cos((M+1)*Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin((M+1)*Pi*x/a)+sin(Pi*y*N/b)*sin((M+1)*Pi*x/a)+sin(Pi*y/b)*sin((M+1)*Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))+(1/4)*(-cos(Pi*y*N/b)*sin(Pi*y/b)*sin(Pi*x/a)-sin(Pi*y*N/b)*cos(Pi*y/b)*sin(Pi*x/a)+sin(Pi*y*N/b)*sin(Pi*x/a)+sin(Pi*y/b)*sin(Pi*x/a))*`w__m,n`(t)/((cos(Pi*x/a)-1)*(cos(Pi*y/b)-1))

(7)

diff(`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), t)-`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(F(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`) = `&PartialD;`(W(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), j = 1, () .. (), N

(D(`&PartialD;`))(T(x, y, t))*(diff(T(x, y, t), t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)-`&PartialD;`(T(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+2*`&PartialD;`(U(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`)+`&PartialD;`(F(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`) = `&PartialD;`(W(x, y, t))/`&PartialD;`(`#mscripts(mi("q"),mi("j"),none(),none(),mo("&period;"),none(),none())`), j = 1, () .. (), N

(8)

NULL


 

Download L_Maple

 

 

An hour or two ago, I answered a question in which it was a question of plotting a complex-valued function of 2 real variables. But the question itself and also my answer to it disappeared somewhere. Therefore, I send my answer here below.

There are two options for plotting:
1. Graphs of real and imaginary parts (as 2 surfaces in 3D).
2. Graph of the absolute value of this function (one surface in 3d) .

restart;
f:=(1+cosh(2*x))*exp(-4*I*t):
plot3d([Re,Im](f), x=0..1, t=0..1, color=[red,blue]);
plot3d(sqrt(add([Re,Im](f)^~2)), x=0..1, t=0..1, color=green);

 

I want to made a comparison via plots of RK-4, NSFD and LWM.

I have noticed a few times now with Maple 2019. It looses kernel connection when it is sitting there idly. This time I observed it. Had saved a document after an intensive calculation. The memory used was about 30Gig. shortly after saving the cpu fan was running hard. I checked task manager and cpu was cycling to 100%, it was mserever. Then the memory usage droped to about 6gig and message as shown. During this time Maple screen down in the LH corner displayed "Ready", so it didn't think it was doing anything.
 

Dear Community,

I run a MapleSim model from Maple. The simulation runs fine giving me the correct graphical plots, but I wonder how could I obtain also the numerical values of the probes vs. time? Sorry I could not figure it out. A matrix format would be perfect: 1st column time, the other columns probe 1 .. n values vs. time. (Files attached)

Tx for the kind help in advance,

best regards

Andras

RunMapleSim.mw , RCNetwork.msim

Hello,

How I can take variation from left-hand side of  5, and reach to right-hand side of  5. After by using integral by part obtained  7?

Thank you

Maple pdsolve supports periodic boundary conditions. So I was hoping it will be able to solve the heat PDE inside disk with periodic boundary conditions. But I am not able to make it work. 

Is there a trick to make Maple solve this, is there something I need to add or adjust something else? or it is just the functionality is not currently implemented?

This is what I tried

restart;

pde := diff(u(r,theta,t),t)=diff(u(r,theta,t),r$2) + 1/r*diff(u(r,theta,t),r)+1/r^2*diff(u(r,theta,t),theta$2);
bc1 := u(a,theta,t)=0;
bc2 := eval(diff(u(r,theta,t),theta),theta=-Pi)=eval(diff(u(r,theta,t),theta),theta=Pi);
bc3 := u(r,-Pi,t)=u(r,Pi,t);
ic  := u(r,theta,0)=f(r,theta);
sol := pdsolve([pde, bc1,bc2,bc3, ic], u(r, theta, t), HINT = boundedseries(r = 0)) assuming a>0,r>0

I solved this analytically by hand using standard separation of variables method. The issue of telling Maple the solution is bounded at center of disk, I assume is being handled automatically by the HINT=boundedseries(r = 0).

If I remove the hint, it also does not solve it. 

Maple 2019, Physics package 338

Hellow, help required to remove the errors

 How to  obtain the pressure drop i am unable to get the output. I am uploading the file  and the equations

help_dp.mw

 

 

 

 


 

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