Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

How I can differential with respect to the constant Amnr], Bmnr], Cmnr]


 

e := mu*(((cosh(eta)-cos(theta))/a)^2*(diff(`U__η`(eta, `ϕ`, theta), eta, eta))+(1-cosh(eta)*cos(theta))*(cosh(eta)-cos(theta))*(diff(`U__η`(eta, `ϕ`, theta), eta))/(a^2*sinh(eta))+2*sinh(eta)*(cosh(eta)-cos(theta))*(diff(`U__θ`(eta, `ϕ`, theta), theta))/a^2)

T := proc () options operator, arrow; rho*omega^2*(int(int(int((u(eta, `ϕ`, theta)^2+v(eta, `ϕ`, theta)^2+w(eta, `ϕ`, theta)^2)*a^3*sinh(eta)/(cosh(eta)-cos(`ϕ`))^3, theta = a .. b), eta = c .. d), `ϕ` = e .. f)) end proc

u__trial := proc (eta, `ϕ`, theta, M, N) options operator, arrow; sum(sum(sum(A[m, n, r]*u[m, n, r](eta, `ϕ`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc; v__trial := proc (eta, `ϕ`, theta, M, N) options operator, arrow; sum(sum(sum(B[m, n, r]*v[m, n, r](eta, `ϕ`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc; w__trial := proc (eta, `ϕ`, theta, M, N) options operator, arrow; sum(sum(sum(C[m, n, r]*w[m, n, r](eta, `ϕ`, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc

proc (eta, varphi, theta, M, N) options operator, arrow; sum(sum(sum(C[m, n, r]*w[m, n, r](eta, varphi, theta), n = 1 .. N), m = 1 .. M), r = 1 .. R) end proc

(1)

L := e-T()

"(∂)/(∂ A[m,n,r])L"

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``


 

Download

 

How I can plot torus structure in the following code instead of cylindrical.

Thanks.


 

"U[1,6](x,theta):=0.03215257166 (sin(-2.350000000+9.400000000 x)-0.1369508410 sinh(-2.350000000+9.400000000 x)) cos(6 theta):"

 

 

with(plots)

[animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]

(1)

cylinderplot(U[1, 6](x, theta)-.1, theta = 0 .. 2*Pi, x = 0 .. .5, grid = [50, 50])

 

torus

torus

(2)

``


 

Download toro.mw

 

 

\Hello,

How I can solve this algebraic to find unknowns ABCD?

I want to gain ABCD automatically without input the coefficients in rule by hand.

Because I should run the code for many input data

Thanks


 

restart;

l:=0.5;a:=0.1; rho:=2700;h:=.0005;
E:=72.4*10^9;v:= 0.3;
n:=6;
m:=1;

AD:=10;
mu:=(2*a*2.35)/l;
nu:=sin(mu*l/(2*a))/sinh(mu*l/(2*a)); omega[m,n]:= 3067.173621;

.5

 

.1

 

2700

 

0.5e-3

 

0.7240000000e11

 

.3

 

6

 

1

 

10

 

.9400000000

 

.1369508410

 

3067.173621

(1)

 

E:=1:k[1,1]:=-5.660173062*10^10:k[1,2]:=-2.8552873062*10^10:k[1,3]:=-8.68528173062*10^10:k[1,4]:=-7.6788528173062*10^10:k[1,5]:=-1.52568528173062*10^10:k[2,1]:=-15.660173062*10^10:k[2,2]:=-21.8552873062*10^10:k[2,3]:=-18.68528173062*10^10:k[2,4]:=-71.6788528173062*10^10:k[2,5]:=-10.52568528173062*10^10:
k[3,1]:=-5.65257260173062*10^10:k[3,2]:=-27.8552552873062*10^10:k[3,3]:=-81.6854428173062*10^10:k[3,4]:=-9.67858528173062*10^10:k[3,5]:=-3.52568528173062*10^10:
k[4,1]:=-51.111660173062*10^10:k[4,2]:=-21.811552873062*10^10:k[4,3]:=-18.68528173062*10^10:k[4,4]:=-17.6788528173062*10^10:k[4,5]:=-11.52568528173062*10^10:
k[5,1]:=-6.660173062*10^10:k[5,2]:=-61.852873062*10^10:k[5,3]:=-82.68528173062*10^10:k[5,4]:=-72.6788528173062*10^10:k[5,5]:=-21.52568528173062*10^10

-0.2152568528e12

(2)

 

 

S:=(Matrix([[rho*h*omega[m,n]^2+k[1, 1],k[1,2],k[1,3],k[1,4]],[k[2,1],rho*h*omega[m,n]^2+k[2,2],k[2,3],k[2,4]],[k[3,1],k[3,2],k[3,3]+rho*h*omega[m,n]^2,k[3,4]],[k[4,1],k[4,2],k[4,3],k[4,4]+rho*h*omega[m,n]^2]])).(Vector(1..4,[[A],[B],[C],[D]]))=-E*(Vector(1..4,[k[1,5],k[2, 5],k[3,5],k[4,5]]));

(Vector(4, {(1) = -0.5658903042e11*A-0.2855287306e11*B-0.8685281731e11*C-0.7678852817e11*D, (2) = -0.1566017306e12*A-0.2185401729e12*B-0.1868528173e12*C-0.7167885282e12*D, (3) = -0.5652572602e11*A-0.2785525529e12*B-0.8168417280e12*C-0.9678585282e11*D, (4) = -0.5111166017e12*A-0.2181155287e12*B-0.1868528173e12*C-0.1767758280e12*D})) = (Vector(4, {(1) = 0.1525685282e11, (2) = 0.1052568528e12, (3) = 0.3525685282e11, (4) = 0.1152568528e12}))

(3)

``


 

Download solve.mw

 

 

 

The worksheet below animates the flattening of a tetrahedron by expanding one of its faces, namely its triangular base.

I would like to animate the flattening of an octahedron so that it assumes the 2D figure resembling the Morley triangle which is included in the worksheet.

Are there documents on the web explaining the technique for doing so? Is there a Maple worksheet available on the web demonstrating the desired animation?

Flatten_a_tetrahedron.mw

n is a Carmichael number iff for every prime factor p of n, p-1/n-1.

Question: How to find odd squarefree composite numbers n having k distinct prime divisors, and the property that exactly k-1 prime divisors satisfy the Carmichael requirement, p-1/n-1 ?

Examples: 231,1045,1635. In these cases k=3 and the prime divisors satisfying the criteria are the greatest and smallest. I have a code for this but would like to compute the general case, where the criteria is satisfied for precisely any k-1 divisors.

Any assistance greatly appreciated.

David. 

 

Is there any maple function to test whether infinite sums and integrals can be swapped say for example whether

this is true? for a given f(x):

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Thanks a million in advance,

Best,

Jie

 

 

In some previous version of Maple there was a function to convert an approximate numerical value, say 1.77245,

to the exact value (if it exists and is short), say sqrt(Pi). I cannot remember the name of this function. Is it still in Maple?

Thanks for any help

Pavel

restart; interface(rtablesize = 10): _EnvHorizontalName := 'x': _EnvVerticalName := 'y': eqPA := (y-b0)/(x-a0) = k: solPA := y=solve(eqPA, y): #k coefficient directeur de PA eqPB := (y-b0)/(x-a0) = -1/k: solPB :=y= solve(eqPB, y):#PB perpendicalaire à PA xA := solve(subs(y = 0, eqPA), x): yB := solve(subs(x = 0, eqPB), y): eqAB := x/xA+y/yB = 1; x k y k eqAB := --------- + --------- = 1 a0 k - b0 b0 k + a0 t := solve(a*(xM+(1/2)*t*a)+b*(yM+(1/2)*t*b)+c = 0, t); 2 (a xM + b yM + c) t := - ------------------- 2 2 a + b #Recherche des coordonnées de la projection d'un point sur une droite D #M(x,y)un point quelconque du plan, M'(x',y') son symé trique dans la symétrie orthogonale d'axe D #le vecteur MM' est colinéaire du vecteur normal n de D; vec(MM')=t.vec(n), n=

Hi! I can´t see what i´m doing wrong! :( Thank you for your help!!!

Hello everyone, here i Denmark we are using comma as a separator for decimal numbers. I have looked in the forum and found that if i changed my region in windows settings, but it is Denmark. When i use number formatting it tells me the output will be with comma as a separator,  but the output comes out with period as the separator. Is there a way to change it manually ?

 

 

I am interested in the root of the equation ((2*n-1)*x + 2*n + 1)*x^n = 1 - x, where 0 < x < 1 and n is a large positive integer.  I believe that the root converges to 1 as n goes to infinity.  How does one obtain an asymptotic estimate of the root for large n?

 

Hello fellows,

I am currently using Maple and surprised I can not solve the following problem. I want to use a function as the upper limit of an integral, for example

f(t) := int(1/x, x = 1 .. t) .

Could anyone tell me why Maple won't understand this?

Thank you for your help, I wish you a nice week.

Mac

Hi, 

I am trying to derive solutions for cubic equation using Maple.

Problem I encountered is it automatically cancles and simplifies, I cannot reach to the final form using Maple commands except modifying the equation by myself.

like, 

(-108*q - 12*sqrt(12*p^3 + 81*q^2))^(1/3)/6 into (-q/2 + sqrt(p^3/27 + q^2/4))^(1/3)

Another one, even though I want this fractional form, it becomes other form automatically

(-q/2 + sqrt(p^3/27 + q^2/4))^(1/3) into (-q/2 + sqrt(12*p^3 + 81*q^2)/18)^(1/3)

Thank you.

Hi

how can i find the answer if this integral analytically

int(exp(-b*x)/(exp(-2*b*x)*a+exp(-4*x)),x);

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