Hello,

My code records the values I need, however, I need to implement a modulo of 2*Pi on my result for theta. But this leads to a graph with no plots and I'm not sure how to fix it. Any help is greatly aprreciated! Thank you in advance!

Kind regards,

Gam

Download Poincare_section_Boyd_plot_fixing_theta.mw

bia Man

i've got a list of 6 ODEs with 6 initial conditions:

MH,MS,M,a,G,e,afb are just constants

Eqns2 := diff(xH(t), t) = vxH(t),
            diff(vxH(t), t) = -G*M*xH(t)/(xH(t)^2+yH(t)^2)^(3/2),
            diff(yH(t), t) = vyH(t),
            diff(vyH(t), t) = -G*M*yH(t)/(xH(t)^2+yH(t)^2)^(3/2),

            diff(theta(t), t) = omega(t),

            diff(omega(t), t) = -G*MS*afb^2*(xH(t)*sin(theta(t))-yH(t)*cos(theta(t))*            (xH(t)*cos(theta(t))+yH(t)*sin(theta(t)))/(xH(t)^2+yH(t)^2)^(5/2):

ICs2 := xH(0) = a*(1+e), vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e))), yH(0) = 0, 0 < theta(0), theta(0) <= Pi,        omega(0) = 10*Pi/T_H:

soln2 := dsolve({Eqns2, ICs2}, {omega(t), theta(t), vxH(t), vyH(t), xH(t), yH(t)}, numeric)

But it doesn't solve it , but instead displays this error message:

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

Can someone find a syntax error or a typo that would explain this?

When assigning a color to a given wave length I initially used ColorTools WavelengthToColor. Acer commented that this wasn't the most accurate. I looked into this a little further and it seems there could be a better result. The attached document compares some different ways of assigning colors to wave lengths. 

Warning- The CIEDE2000 computation for deltaE is very slow. I think this is because of the hue angle calculations which use piecewise a lot. The CIE94 delta E method produces nearly the same result and takes minutes instead of hours.

Questions;

 I think I could speed up my calculation if I could find the position of the minimum element of an Array similar to FindMinimalElement of a list. 

I created my own atan2 function (similar to Excel). If there were a built in Maple equivalent perhaps it would be faster? I didn't see any such function.

6bit_Wavelength_Color_CIEDE2000.mw

Hello,

I have a procedure which plots a graph. I need the x-axes, which in this case is theta, to range between -3 and +3. However, I am not sure as to how I can create this restricted range. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download Poincare_section_Boyd_plot.mw

Download Poincare_section_Boyd_plot.mw

Hi,

Wondered if anyone could help with the query below.

Consider f(x,y) defined as:
f := proc (x, y) options operator, arrow; x*y/(x+y) end proc

Then f(A, B); becomes:
(A * B )/(A + B)

now consider the polynomial:(poly2)

poly2:=(A*B+A*X+B*X)*(Y+X)/((A+B)*X*(2*Y+X))

This polynomial is just the expansion of the polynomial below (lets call it poly1) which MAPLE does not recognize.

(A*B/(A+B)+X)/(X+Y*X/(Y+X))

Here you can see that A,B on top and X,Y on the bottom are clearly of the form f(x,y).

Is there a way you can get MAPLE to recognize certain algebraic forms such that the polynomial poly2 could be written either as poly1 (already shown above) or as poly3 below:

poly3:=(f(A, B)+X)/(X+f(Y, X))

I have tried using simplify in the following form but not much luck. It doesn't seem to recognize anything other than the obvious.

simplify(poly2, {A*B/(A+B) = F1}, tdeg(A, B))

(I am still a bit new to the MAPLE syntax and procedures so apologies if I have missed something obvious function that can do this.)

Thanks.

In Maple 2015, the DrawNetwork command option "horizontal" does not seem to work. Is this a bug? It doesn't even display horizontally on the online Maple Help webpage. Any help would be appreciated.

Hello,

I have a question about poincare sections. I have this piece of code i need to analyse and I want to use a poincare section in order to so. How could I do it? I am interested in theta and omega. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download New_Poincare_section.mw

Since we’re almost at the end of the year, I thought it would be interesting to look back at our most popular webinars for academics in 2015. I found that they fell into one of two categories: live streaming webinars featuring Dr. Robert Lopez and Maple how-to tutorials.  (If you missed the live presentation, you can watch the recordings of all these webinars below.)

The first and second most popular webinar were, unsurprisingly, both of the live streaming webinars that featured Dr. Robert Lopez (Emeritus Professor at Rose Hulman Institute of Technology and Maple Fellow at Maplesoft). These webinars were streamed live to an audience and allowed many people to get their first glimpse of the man behind the Clickable Calculus series and Teaching Concepts with Maple:

1.       Eigenpairs Enlivened

In this webinar, Dr. Robert Lopez demonstrates how Maple can enhance the task of teaching the eigenpair concept, and shows how Maple bridges the gap between the concept and the algorithms by which students are expected to practice finding eigenpairs.

2.       Resequencing Concepts and Skills via Maple's Clickable

In this webinar, Dr. Lopez presents examples of what "resequencing" looks like when implemented with Maple's point-and-click syntax-free paradigm. Not only can Maple be used to elucidate the concept, but in addition, it can be used to illustrate and implement the manipulations that ultimately the student must master.

The next three were all brief webinars on how to complete specific tasks in Maple 2015. Just under a dozen of these were created in 2015 and they were all quite popular, but these three stood out above the rest:

3.       Working with Data Sets in Maple

This video walks through examples of working with several types of data in Maple, including visualizing stock and commodity data, forecasting future temperatures using weather data, and analyzing macroeconomic data, such as employment statistics, GDP and other economic indicators.

4.       Custom Color Schemes in Maple

This webinar provides an overview of the colorscheme option for coloring surfaces, curves and collections of points in Maple, including how to color with gradients, according to function value or point position. Examples of how the colorscheme option is used with various commands from the Maple library are also demonstrated.

 5.       Working with Units in Maple

Maple 2015 allows for more fluid and natural interaction with units. This webinar provides an overview of the new unit formatting controls and new Temperature object, and demonstrates how to compute with units and tolerances.

Are there any topics you’d like to see Robert cover in upcoming webinars? Or, any Maple how-to videos you think would be a helpful addition to our library? Let us know in the comments below!

Kim

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Physics/.

i see bra and ket expression are so beautiful,

however,

how do real valued eigenvectors involve in calculation of bra and ket style computation?

assume a,b,c,d,B2,B3 are matrices and y is unknown

eq2 := a*b+c*d+a;
eq3 := a*c+c*d+c;
eq4 := a*b+c*a+b*c;
eq5 := a*b+a*d+b*c;
solve([eq2=B2,eq3=B3,eq4=B2,eq5=y],[a,b,c,d]);

which function can solve this kind of system of matrices?

how to solve a,b,c,d in terms of y?

solve([a = -(-y+1)/(x-y+2), b = -(-x^2+2*x*y-y^2-3*x+3*y-2)/(x-2*y+3), c = -(x*y-y^2-2*x+4*y-4)/(x*y-y^2-x+2*y-1), d = -(-x*y+y^2+x-2*y+1)/(x-2*y+3)], [x,y]);

i do not know whether multiple solutions lead no solutions in this.

if so, is it possible to show all possible solutions of x and y in terms of a,b,c,d ?

Download Bryson_sesson1_p6.mw

I have an implcit function to plot. I can plot it with the parameter but that puts the parameter on the x axis instead of the y axis. What is the best way to present the plot with the parameter on the y axis?

T; R0 := 0.1003183099e-5; T;
/ / -15 -34
- \0.00007363071999 h \3.947841762 10 h + 3.158273412 10

-7 \\// (1/2)
- 3.947841763 10 h R0// |/ 2 -7 \
\\-Pi h + 1.256637062 10 R0/

\
2 / -15 -7 \|
R0 \-1.256637062 10 + 1.256637062 10 R0//
0.000001003183099
1 / 20 /
- --------------------------------- \5.862184047 10 h \4.00
(1/2)
/ 2 -13\
\-Pi h + 1.260637062 10 /

-16 2 -13 -34\\
10 Pi h - 1.260637062 10 Pi h + 3.158273412 10 //
plot(T, h = 0.1e-8 .. 0.10e-7, title = Tension*vs*height*of*dome*above*plane, labels = [m, N/m]);

I would like the plot to be inverted to show the height of the dome as a function of tension;

Maple's isprime is not a definitive primality test. The input has to pass a "strong pseudo-primality test" and "one Lucas test". This is well documented. I thought I remembered that there is also a way to get Maple to perform a true primality test, but I don't remember how and don't see anything about this in the Maple help system.

Is my memory faulty, or is there no definitive primality test in Maple?

Thanks in advance,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu

Hei, I'm trying to create a random walk in the plane, with constant step length (=1) and the angle between two consecutive steps are decided by a probability density function. I just can't seem to find out how I should implement the density function into my worksheet.

The probability density function is: p(phi)=(1/4)*cos(phi/2), on the interval [-Pi,Pi].
And  I think i managed to do it by selecting a random angle, but don't know how to generate a random angle given this probability function. Any ideas? It'd be highly appreciated!