On and off over the last few months I've been meaning to learn about computing a center manifold approximation and normal form of a dynamic system of three differential equations.

My main reading: Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Second Edition, Springer, 2003.

I want to apply the technique to a system I derived from an optimal control problem. As a first step, I decided to reproduce the steps for the following system, for which the solution has been published.

Below is the latest version of the code to draw iso-chrone lines and a salvo of arrows onto the phase diagram of a two-dimensional system of ordinary differential equations.

I have greatly benefited from inputs by Robert Israel (who wrote the first incarnation of the procedure), Joe Riel, and pagan. A big thankyou!

The procedure is sufficiently developed for my current purpose, so I don't plan to modify it much in the near future.

Tested on Maple 13/ Classic. The last plot combines the isochrones and the salvo.

Is there some palettes to choose font (size) more convenient?

can I set the defaut size of "Heading 1","Serif",size 18 as 14,for example.

question2:ctrl+period hotkey doesn't work.

 

If I do:

with(CurveFitting):

xydata:=[[0,1],[1,5],[3,9]]:

RationalInterpolation(xydata,x);

I get a rational funciton that goes through those points.

 

What I want to do is interpolate the following function of x:

evalf(int(exp(-a^2 + x),a=0..5);

So, now instead of:

xydata:=[[0,1],[1,5],[3,9]]:

I have something like:

I want to get a common divisor from multinomial,such as (b-a), can I use the order collect (S,(b-a)),maybe it is wrong,what others I can use?

thank you

Hi, I want to create an array as following:

Array(0 .. t, 1 .. 2)

I need to initialize it with <i, 0> where i is the index of each element. The Maple help suggests to use a "set of equations of the form (indices) = value". But I have no idea what that actually means. "(indices) = value" is totally unspecific to me. I guess I have to name the indices first or something like that...

Thanks in advance.

some ODEs can be solved by using different methods,how does maple chosse the methods?

integrating fator problems

question2:what's the error I made in solving the following ODE step by step? the second method and answer is right.

question3:Can Maple automatically add multiplication sign instead of spaces?

what I learned today is that you cannot write 1e-i, where i is an unassigned variable (at least not like that):

convert to ln(e) to 1

maybe I've asked some similar questions several days ago,

In mathematica when I type:

Manipulate[Plot[Sin[c*x], {x, 0, 10}], {c, 1, 5}]

I get a 2D plot of sin(c*x) for x between 0 and 10, with c =1.

Then with the mouse I can drag a bar which will show what happens when c changes between 1 and 5. I can drag that bar to the particular c value for which the plot looks the way I want.

 

In Sage this can be done using the @interact command.

 

Is there an analog for this sort of thing in Maple ??

 

Thanks a lot!

We can pull values of a list

a:=[2,5,g,f,5,h];
 

a[3];
                g

a[2];
                5

etc... but it doesn't work in reverse.  You can't place a value in a certain position in a list

Hello,

does the verify command not work for trig functions ??

verify(sin(x)/cos(x),tan(x),'equal')

gives 'FAIL' rather than 'true'

 

Is there a function for checking whether or not the LHS and RHS of my trig identity match ??

 

 

I'm running a relatively complicated maple file on my mac computer and it's give me the following error message: Kernel connection has been lost. The Kernel returned the following error message: Execution stopped: Memory allocation failed. Please see? alloc for more details. you should sace this worksheet and restart Maple kernel. Firewalls have been known to cause problems with kernel connections in Maple. Please ensure that any firewall software is configured to allow Maple to creat connections to the kernel.

I'm posting it here to keep a record for myself.

my second blog post, aka "the lost blog post", is here.

Still some way to go. The following still needs to be tweaked case by case. And it can be made more compact too. Are the arrows flying so much faster in the top triangular area or are the arrows not printing where I expected them to ...

I am trying to create a 3d plot of a simple function which evenly distributes a force around the end of a pipe as a function of it's angle.  The equation is

fy :=FORCE/(2*Pi*R)*COS(PHI), PHI=0..2*Pi, R = CONSTANT

I would like to create a wire-frame, shaded, cylindrical plot showing the variation in force as a function of the angle phi.

Thank you in advance for your assistance.