When solving a nonlinear differential equation on some variable x, but using some other parameter w, I am finding on Maple some complicated solution, which I would like to simplify by making evident what is the x dependence, and where I can compact complicated functions of the parameter w alone into new constants. How can I do that automatically?

For example, to have

(sinh(w) + ln(w))*x 

to be automatically called

c*x

Thank you in advance.

Hello.

given this expression

T:=unapply((1/6930)*exp(-(1/7938)*(X[4]-933)^2)*exp(-(1/6050)*(X[2]-805)^2)/((1+exp((1/50)*X[4]-(1/50)*X[2]))*Pi),X[2]);

U := unapply(sum(T(X[2]), X[4] = 0 .. 3600), X[2]):

I want to display U, but not all 3600 terms. is there anyway to simplify/reduce this sum?

kind of like geo series a+ar+ar^2+ar^3+...+ar^(n-1)=sum(ar^k,k=0..n-1) can be reduced to a*(1-r^n)/(1-r)

Hello. Earlier, I asked about it, (see http://www.mapleprimes.com/questions/203573-How-To-Do-Simple-Operations-On-Tensors). However, not all I was able to understand. Below I will give a try, and maybe you'll show me where I'm wrong.

Also, I'm interested in how you can determine the components of the tensor in a different coordinate system connected with the original in any conversion. Thank for your help.

Download 1.mw

I am trying to explore the equality of two lengthy expressions. Unfortunately, my relations that all are symbolic, are lengthy and I use 'verify' command to explore the equality of them. When I use this command the 'FAIL' message appears. Maybe it is because of lengthy expressions and Maple cannot exploring equality of them. I have attached the corresponding file. Does anyone know what's the real problem? Thanks in advance.

MMatrix.mw

Hello, 

is there a way I can use data (variables) from Maple environment in the Maplesim environment. 

I have a scirpt in maple that generates the robots joints angles and need to use them in the 3D robot built in maplesim. I know I can export/Import data, but this sounds redundant. Is there a way to simply use an input block as a source of the data in maplesim and have the variable name generated in maple used int. Similar to what Matlab/Simulink does.. 

thanks.

Могу ли я использовать Клен, чтобы найти конкретные решения, которые выражаются либо в начальных и эллиптических функций для систем обыкновенных дифференциальных уравнений. Например, вы можете получить в Maple решений (sub_Solve01, sub_Solve02) для систем, которые перечислены в файле?
exp01.mw

hello
i have a problem that you could help me
i have an expression that i want convert it to an expression according to the expression q[d] with maple
i have bellow expressions
B[d]:=(-d*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2))
B[o]:=(-2*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2))
A[o]:=w[1]*(alpha[o]-c[o]-t[o])+2*w[2]*e[o]
A[d]:=w[1]*(alpha[d]-c[d]-t[d])+2*w[2]*e[d]
q[o]:=B[o]*A[o]-B[d]*A[d]
q[d]:=B[o]*A[d]-B[d]*A[o]
i want simplify expression U[d] such as this one
U[d]:=w[1]*(q[d]*(alpha[d]-q[d]-d*q[o]-c[d]-t[d])-C)+w[2]*(e[d]*q[d]+e[o]*q[o])+w[3]*((1/2)*(q[d]+q[o])^2)
I'm looking to simplify U[d] according to the expression q[d]
please please help me

Download loop.mw

Hey,

Basically the problem is that when I try to derive a variable L, which is defined by a very big equation, Maple does not do the maple. But if I copy and paste the big equation it calculates everything perfectly. Could I get any insight on why is that?

The copy paste method is very space consuming.

Thanks in advance.

I have a system of pdes and solved numerically using pdsolve (numeric) command.

The system consists of four first order partial differentia equations.

for example u(x,t), R(x,t)....

what command should I give to the Maple and get the graph of u(x,t) at a specific point x_0?

For example, I need a plot for u(30,t).

Is it possible with the maple plot?

I really appreciate your help.

Thank you for reading this post. :)

Dear friends! Hope you will be fine. I want to generate a general form of the matrix (of order 2M+1 by 2M+1) shown below in Maple

[[[0,0,⋯,0,-1/(M Pi),0,⋯,0,1/(M Pi)],[0,0,⋯,0,-1/((M-1) Pi),0,⋯,1/((M-1) Pi),0],[⋮,⋮,⋱,⋮,⋮,⋮, ⋰,⋮,⋮],[0,0,⋯,0,-1/(Pi),1/(Pi),⋯,0,0],[1/(Pi),1/(Pi),⋯,1/(Pi),1,1/(Pi),⋯,1/(Pi),1/(Pi)],[0,0,⋯,1/(Pi),1/(Pi),0,⋯,0,0],[⋮,⋮,⋰,⋮,⋮,⋮,⋱,⋮,⋮],[0,1/((M-1) Pi),⋯,0,1/((M-1) Pi),0,⋯,0,0],[1/(M Pi),0,⋯,0,1/(M Pi),0,⋯,0,0]]]

for M=4 we get

Matrix(9, 9, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = -(1/4)/Pi, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = (1/4)/Pi, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = -(1/3)/Pi, (2, 6) = 0, (2, 7) = 0, (2, 8) = (1/3)/Pi, (2, 9) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = -(1/2)/Pi, (3, 6) = 0, (3, 7) = (1/2)/Pi, (3, 8) = 0, (3, 9) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -1/Pi, (4, 6) = 1/Pi, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (5, 1) = 1/Pi, (5, 2) = 1/Pi, (5, 3) = 1/Pi, (5, 4) = 1/Pi, (5, 5) = 1, (5, 6) = 1/Pi, (5, 7) = 1/Pi, (5, 8) = 1/Pi, (5, 9) = 1/Pi, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 1/Pi, (6, 5) = 1/Pi, (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = (1/2)/Pi, (7, 4) = 0, (7, 5) = (1/2)/Pi, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (8, 1) = 0, (8, 2) = (1/3)/Pi, (8, 3) = 0, (8, 4) = 0, (8, 5) = (1/3)/Pi, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (9, 1) = (1/4)/Pi, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = (1/4)/Pi, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0})

I want the general for of this matrix for any value of M

9_by_9.mw

Hi Guys,

I am trying to solve the folling ODE in maple but am struggling to get to the correct solution. I first of all have the following equations;

Which give me the following;

With thw boundary conditions;

M(l) = 0, M(0) = 0, v(0) = 0, v(l) = 0

The given solution is;

v(x)=(qx/24EI)*(x^3-2lx^2+l^3)

Anything that might point me in the right direction would be great!

Cheers

Steve

conic_section_animation.mw

I have a nice 1 x 2 arry of plots, both columns of which are animations. They play beautifully inline. However, I cannot get them to export. Only one column can be selected at a time, hence I could export each animation separately, but the whole idea is to watch the animations together, side-by-side.

I have tried to change the plot setup to export to a file but when I do that I get an error in plots[display].

See the file above for details.

It could be that Display just cannot do this. But I don't see why not. I can export an array of plots of static images and it creates a single GIF file with both columns. The animated gifs should just be this same idea done 50 times over.

Any advice?

Dear community,

The VectorCalculus package in Maple 18 exhibits some rather odd behaviour when calculating an integral over a 3D-domain (an elipsoid centered at (0,0,1) with length of semi-axes 2, 2, and 1) given by a 'Region'. It also reports an incorrect result when calculating the flux of a vector field through the surface of this ellipsoid.

See below for a minimal working example:

// integrate several functions over ellipsoid

int(2*x+2*y, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: 0

int(2*z, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: 32*Pi/3

int(2*x+2*y+2*z, [x, y, z] = Region(-2 .. 2, -sqrt(-x^2+4) .. sqrt(-x^2+4), -sqrt(1-(1/4)*x^2-(1/4)*y^2)+1 .. sqrt(1-(1/4)*x^2-(1/4)*y^2)+1));    ---- output: -32*Pi/3

Why does the integral change sign?

// Calculate flux of vector field over surface of ellipsoid

F2 := VectorField(`<,>`(x^2, y^2, z^2));

S2 := Surface(`<,>`(2*sin(t)*cos(s), 2*sin(t)*sin(s), 1+cos(t)), s = 0 .. 2*Pi, t = 0 .. Pi);

Flux(F2, S2, 'outward');   ---- output: -32*Pi/3

However, since 'z' is positive over the entire ellipsoid, by the Divergence Theorem we know the result should be positive (in fact, equal to +32*Pi/3). Changing 'outward' to 'inward' does not change the sign, by the way.

Is this a bug inside the VectorCalculus package which appears more often, or have I done something wrong?

Thank you for responding and apologies if a similar question has already been answered in another thread.

Best wishes,

QQ

Hello all,

I am trying to solve a simple PDE with one unknow theta and three boundary conditions. Unfortunately, I receive error messages. In this case, the integer s seems to cause troubles. The error message is:

Error, (in pdsolve/numeric/process_PDEs) variable(s) {s} are in the PDE system but are not dependent or independent variables

When I assign s a value (such as 1 or 2), no error messages, but still no response. I get:

pds:=module() export plot,plot3d,animate,value,settings; ... end module

Would anyone have an idea how to resolve this issue? Thank you for your suggestions. Below is the small portion of code

restart;
with(PDEtools);

PDE := [(1-y^(s+1))*(diff(theta(y, z), z)) = diff(theta(y, z), `$`(y, 2))+y^(s+1)*(s+1)^(1/s+1)];
IBC := {theta(1, z) = 0, theta(y, 0) = 0, (D[1](theta))(0, z) = 0};

pds := pdsolve(PDE, IBC, numeric);
Error, (in pdsolve/numeric/process_PDEs) variable(s) {s} are in the PDE system but are not dependent or independent variables