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Dear all;

 

I need a help in this question.

u(x,y,t) my solution of PDE. x,y space, and t=time.

In the case without t. .i.e. u(x,y). Here is a visualization of the lattice u(x_i,y_j). i=1..3, anf j=1..3.  Please try this example, it's working. 

my question, if i would like to add a third variable t, i.e.  and get u(x_i,y_j,t_k)  on each points. I would like to show the lattice in (x,y) plan for each t_k. I Think I will get many parallel lattice. 

Please can some one, modify this code to get the parallel lattice. Thanks.


with(LinearAlgebra):
with(plots):
with(PDEtools):
interface(rtablesize=20):

Here,


L := 'L':
N := 'N':
g := 'g':
Z := i -> -L+2*L/(N+1)*i;
x[0] = Z(0),x[N+1] = Z(N+1),y[0] = Z(0),y[N+1] = Z(N+1);

 

N := 4;
L := 1;
r := L/(N+1)/4;
ngon := (n,x,y,r,phi) -> [seq([x+r*cos(2*Pi*i/n+phi), y+r*sin(2*Pi*i/n+phi)], i = 1 .. n)]:
p[1] := display([seq(polygonplot(ngon(4,Z(0),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(N+1),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(i),Z(0),r,0),color=magenta),i=1..N),

seq(polygonplot(ngon(4,Z(i),Z(N+1),r,0),color=magenta),i=1..N),

seq(seq(polygonplot(ngon(20,Z(i),Z(j),r,0),color=white),i=1..N),j=1..N),

textplot([seq(seq([Z(i+0.1),Z(j),typeset(u[i,j])],i=0..N+1),j=0..N+1)],align={above,right})],view=[Z(-1)..Z(N+2),Z(-1)..Z(N+2)],tickmarks=[[seq(Z(i)=typeset(x[i]=evalf[2](Z(i))),i=0..N+1)],[seq(Z(i)=typeset(y[i]=evalf[2](Z(i))),i=0..N+1)]],

axes=boxed,scaling=constrained,labels=[``,``]):
p[1];

 

 

 

 

 

 

Hello Maple users friends,

I have two lines in the space (x,y,z) described by the equations in L1 and L2:

 

L1:= {4*x + 3*y + z = 0, x + y - z - 15 = 0}:

L2:={12*x + 5*y + 7*z -13 = 0, 9*x + y -3*z - 5 = 0}:

I would like the get the parametric (with z=t) equations P1 and P2 of the two lines..

I see the "form" of such parametric equations P1 and P2 using "solve"

solve(L1, {x, y}); solve(L2, {x,y});

 

but I do not know how to use those values to get my parametric equations P1 and P2 to continue with additional computation (area, volume etc).

Thanks for your attention and help.

JJ

hello guys , i have a 3D dynamical system , what can i do to have its phase space in poincare coordinates ? thanks so muchmaple.mw

Hi all,

There is a state space system as follows:

X_dot = A.X + B.U

Y = C. X

The transfer function of this system is

H(s) = C. (sI-A)-1.B                 (1)

H(s), that is calculated in Maple by using the formula (1), is very complex (please see the attached file).

Would you please show me how to find the transfer function of the system? 

In addition, how to plot its bode plot?

Hello all,

I have the state-space form of a dynamics sytem:

X_dot = AX+B.U

Y= C X,

The initial conditions of the outputs (Y0) are also given.

A is 7x7 known matrix,

C is 14x7 known matrix,

B = 0;

The problem is that it's too long to write down every equations (14+7 eqns) and variables in "dsolve" function

Would you please show me the shorter way to solve a very large state-space system?

I really appreciate your help.

Space After New String...

January 17 2013 aa 15

Why does Maple put space after a new string?

How to prevent Maple from doing that?

Screenshot

Critical Points...

November 25 2012 escorpsy 15

Dear Markiyan Hirnyk 

From  Phase-space trajectories i mean below photo which the asterisk arecritical points. but how can i compute the critical points and their nature ( stable , unstable , saddle) with maple ?

Thank for your time

 

Jacobe

How to extract affine terms from a differential equation after linearization?

Vanderpol Eqn:

diff(x[1](t),t)=x[2](t)

diff(x[2](t),t)=(1-x[1](t)^2)*x[2](t)-x[1](t)

 

To be precise, I linearized...

On Monday, August 6 at 1:31 a.m. EDT, NASA will attempt the landing of a new planetary rover, named Curiosity, on the surface of Mars.  The Mars Science Laboratory project is managed by the NASA Jet Propulsion Laboratory (JPL) in Pasadena, California, a world-renowned center for robotic space exploration and advanced science and engineering.  JPL recently began a widespread adoption of Maplesoft technology, and Maplesoft’s products are expected to help JPL save...

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