Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

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

with(plots):

a := 1.501*10^9:

Th := sqrt(4*Pi^2*a^3/(G*(Mh+Msat)));

1876321.326

 

0.3348672330e-5

(1)

HyperionOrbit := proc (`θIC`, `ωIC`) local a, Mh, Msat, G, e, beta, M, Eqns, ICs; global `ωH`, Th, soln; a := 1.501*10^9; Mh := 5.5855*10^18; Msat := 5.6832*10^26; G := 6.67259/10^11; e := .232; beta := .89; M := Mh+Msat; Eqns := diff(theta(t), t) = omega(t), diff(omega(t), t) = -G*Msat*beta^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)^2.5, 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); ICs := xH(0) = a*(1+e), yH(0) = 0, vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e))), theta(0) = `θIC`, omega(0) = `ωIC`; soln := dsolve({Eqns, ICs}, numeric); odeplot(soln, [theta(t), omega(t)/`ωH`], 0 .. 5*Th, numpoints = 2000, labels = ["θ(t)","ω(t)/ωH"], axes = boxed, size = [.25, .75]) end proc

``

 

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 ?

 

equ1 := -l*cos(xi)^2*(1-cos(`β__f`))/(alpha^2.sin(sigma))-`λ__2`*w*(v^2.sin(sigma))/(g*l*cos(xi)^2) = 0

-l*cos(xi)^2*(1-cos(`β__f`))/(alpha^2.sin(sigma))-`λ__2`*w*(v^2.sin(sigma))/(g*l*cos(xi)^2) = 0

(1)

equ2 := -l*cos(xi)^2*(1-cos(beta[f]))/(alpha*sin(sigma)*tan(sigma))+Typesetting:-delayDotProduct(l, cos(xi)^2)*z__0*sin(`β__f`)/(alpha*sin(sigma)*(2*l*cos(sigma)^2))-`λ__1`*`#mi("L")`*`#mi("sin",fontstyle = "normal")`(sigma)*cos(xi)+`λ__2`*L*cos(sigma)*cos(xi)-`λ__2`*w*alpha*v^2*sin(sigma)/(g*l*tan(sigma)*cos(xi)^2) = 0

-l*cos(xi)^2*(1-cos(beta[f]))/(alpha*sin(sigma)*tan(sigma))+(1/2)*(l.(cos(xi)^2))*z__0*sin(`β__f`)/(alpha*sin(sigma)*l*cos(sigma)^2)-`λ__1`*`#mi("L")`*`#mi("sin",fontstyle = "normal")`(sigma)*cos(xi)+`λ__2`*L*cos(sigma)*cos(xi)-`λ__2`*w*alpha*v^2*sin(sigma)/(g*l*tan(sigma)*cos(xi)^2) = 0

(2)

equ3 := l*cos(xi)^2*sin(`β__f`)*tan(sigma)/(alpha*sin(sigma)*(2*l)) = 0

(1/2)*cos(xi)^2*sin(`β__f`)*tan(sigma)/(alpha*sin(sigma)) = 0

(3)

equ4 := -`λ__1`*`#mi("L")`*`#mi("cos",fontstyle = "normal")`(sigma)*sin(xi)+`λ__2`*L*sin(sigma)*sin(xi)-2*`λ__2`*tan(xi)*w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)-l*sin(2*xi)*(1-cos(beta[f]))/(alpha*sin(sigma)) = 0

-`λ__1`*`#mi("L")`*`#mi("cos",fontstyle = "normal")`(sigma)*sin(xi)+`λ__2`*L*sin(sigma)*sin(xi)-2*`λ__2`*tan(xi)*w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)-l*sin(2*xi)*(1-cos(beta[f]))/(alpha*sin(sigma)) = 0

(4)

equ5 := L*cos(sigma)*cos(xi)-w = 0

L*cos(sigma)*cos(xi)-w = 0

(5)

`#mi("equ6")` := `#mi("L")`*`#mi("sin",fontstyle = "normal")`(sigma)*cos(xi)-w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)

`#mi("L")`*`#mi("sin",fontstyle = "normal")`(sigma)*cos(xi)-w*alpha*v^2*sin(sigma)/(g*l*cos(xi)^2)

(6)

answer := solve({equ1, equ2, equ3, equ4, equ5, equ6}, {alpha, sigma, xi, `λ__1`, `λ__2`, beta[f]})

``

(7)

``

(8)

NULL

 

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!


Hi everyone, I'm working a problem

Given a dog and a man. At t=0, the position of the man and his dog is (0,0) and (0,h), respectively. Then, the man start moving along Ox with constant speed vm. The dog keep running toward its master with constant speed vd. Describe the movement of the dog?

Therefore, let say the position of the dog is (f1(x),f2(x)), I wrote these:

restart;

with(plots);

MD := proc (h, vm, vd) local x, y, ode, ics, sol;

ode := {(diff(f2(t), t))*(vm*t-f1(t))+(diff(f1(t), t))*f2(t), diff(f2(t), t) = -sqrt(vd^2-(diff(f1(t), t))^2)};

ics := {f1(0) = h, f2(0) = 0};

sol := dsolve(ode union ics);

x := unapply(eval(f1(t), sol), t);

y := unapply(eval(f2(t), sol), t);

plot([x(t), y(t), t = 0 .. 10], scaling = constrained) end proc;

MD(10, 1, 5);

However, "sol" is returned NULL, which means the equation has no solution. I supposed I completed the motion part of the problem correctly. Please help me or point out an another method

 

Thank you in advance for your time.

I can search for any phrase or symbol in my Maple Worksheet but "sign symbol".

I have a very big result that I am not sure how many minus it has. When I search for - sign, no match found. I can see some minus in the worksheet but Maple can not find them.

Please help me.

I really appreciate.

if there is a funciton like f(i,j)=i+2*j
and I have already print out a 3D picture use the commend
"plot3d(f,i=1..10,j=1..10);"
the 3D picture just like the link : http://imgur.com/eLYhYEs
how can I convert the datas in 3D picture to text file?
the type may be like as follow I think.
-------------------------------------
(i,j)=f(i,j)
(1,1)=3
(1,2)=5
(1,3)=7...
-------------------------------------
I had try
"writedata("C:\\desktop\\a.txt",3Ddatas)"
but it seems can only output one variable parameter in a function, what else can I do?
thanks a lot.

Dear all;

I need you to understand this problem...

when i plot the function, using the graph i see that the function is above the x-axis but when I compute some values of this function I get a negative values....like
evalf(y(99.6));  is a negative value, but in the graph it is possible... I don't  undertand the problem...

restart:
with(plots):

# funciton

y:=x->-4.1123583570*10^281*exp(-(2/3)*x^(3/2))/(x^(1/4)*sqrt(Pi))+1.6554662320*10^(-289)*exp((2/3)*x^(3/2))/(x^(1/4)*sqrt(Pi))+(16/153)*x^(7/6)*sqrt(Pi)*exp((2/3)*x^(3/2))+Pi*((1/2)*exp(-(2/3)*x^(3/2))*(-1+exp((2/3)*x^(2/3)))/(x^(1/4)*Pi)-(16/153)*x^(7/6)*exp((2/3)*x^(3/2))/sqrt(Pi)):

#I plot this function in the interval (a,b)

a:=99;b:=100; # interval (a,b)
 forget(evalf): Digits:=20:
P1:=plottools:-transform((x,y)->[x+a,y])(plot(expand(y(x+a)),x=0..1,color=blue)):
forget(evalf): Digits:=4000:
P2:=plot(ysol, a..b, style=point, adaptive=false, numpoints=25, symbol=solidcircle, symbolsize=20, color=blue):
Digits:=20:
plots:-display(P1,P2);
evalf(y(99.6)); 

 Thank you in advantage for your remarks

 

 

how_do_i_get_floating_point_answer.mw

 solve({-(1/3)*(eta+5)/(eta-3) = 3*eta/(-2+eta)})

{eta = 6/5-(1/5)*61^(1/2)}, {eta = 6/5+(1/5)*61^(1/2)}

(1)

I want the answer

eta := 6/5-(1/5)*61^.5

-.362049935

(2)

what is the command i should use? Please help. Thanks.

``

 

Download how_do_i_get_floating_point_answer.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

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