Hi, i want to investigate  chaos for the problem , cantilever beam under random narro band excitation, but the code has errors .the code is this:

      restart:with(plots):      h:=1: Omega:=(0..376):alpha1:=617.2:alpha2:=1.02*10^(8): c:=.002:k:=18.4:  step:=0.1:imax:=376:  for i from 0 to imax do;  Omega[i]:=i*step:   f:=evalf(solve({((-a*Omega[i]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega[i]^(2)*a^(3)-(3)/(4)*k*Omega[i]^(2)*a^(3))^(2)+(c*Omega[i]*a^())^(2))=h^(2),a>0}));  ff[i]:=((rhs(f[1]))^(2))/(2):  end do:   l1:=[[Omega[n],ff[n]] $n=0..imax]:  p1:=plot(l1, x=0..3,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    jmax:=914: f1:=array(377..914):f2:=array(377..914):f3:=array(377..914):Omega1:=array(377..914):  for j from 377to jmax do;  Omega1[j]:=j*step:   fff:=evalf(solve({((-a*Omega1[j]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega1[j]^(2)*a^(3)-(3)/(4)*k*Omega1[j]^(2)*a^(3))^(2)+(c*Omega1[j]*a^())^(2))=h^(2),a>0}));  f1[j]:=((rhs(fff[1,1]))^(2))/(2):f2[j]:=((rhs(fff[2,1]))^(2))/(2):f3[j]:=((rhs(fff[3,1]))^(2))/(2):  end do:   ll1:=[[Omega1[n],f1[n]] $n=377..jmax]:  pp1:=plot(ll1, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll2:=[[Omega1[n],f2[n]] $n=377..jmax]:  pp2:=plot(ll2, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll3:=[[Omega1[n],f3[n]] $n=377..jmax]:  pp3:=plot(ll3, x=0..15,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):       plot({  seq(seq(p1), seq(seq(pp1),seq(seq(pp2),seq(seq(pp3))  },style=point,title=`Pitchfork Diagram`);  Thanks for your help

Below is a link to my worksheet that evaluates 6 expressions that are presumably equivalent.  However, there seems to be a region for 7<n<100 where the results diverge.  All other values of n yield identical results.  I am at a TOTAL loss as to what is happening.  I hope that someone here might shed some light on this quirk.

divergent_behavior.mw

We conjecture that the polynomial h(n) = n^2 + n + 41 is prime for an infinite number of values n.
We furthur conjecture that p(n) = n^2 + 1 is prime an infinite number of times.

I have shown that the set (x,y) with h(y) mod x is congruent to 0 can be written down.  It is p(x,y).  p(x,y) is the set of all divisors of h(n).  See

https://sites.google.com/site/primeproducingpolynomial/

landau.mw

Regards,

Matt

Am I applying improper syntax for the is command?  Out of the 5 attempts to equate X with the time derivative of S11 only the combine command yields the expected result.  If only combine works then why do the others not work?
 

Download syntax_for_is.mw

Hello Guys,

Can maple derive Einstein field equations from Einstein-Hilbert action ?

Thx

The attached worksheet performs two functions:

(1) It lets me print 4 × 6 Index Cards for the short entries in each table.

(2) It allows for easy storage and retrieval of syntax (code).

The worksheet has many tables, each separated by a Page Break.

Questions:

(a) Is there a way to sort all the different tables so they will be arranged in alphebetical order?

(b) When I select one table to print and open the Print Dialog, the "Selection" option is grayed out. (see graphic below).  (1) Is there a way to enable the selection option?  (2) Is there a way to determine what page I am on so I can use the "Pages from...to" option?  If I need to number the pages, will the page numbers reset to parallel a new alphabetic sort order.

Many thanks in advance.  See WC29_4_BY_6_NOTE_CARDS_UNSORTED.mw attached. And see image of Print Dialog below.

Les

Hello,

How can i solve this integro-PDE(partial diffrential equation)??

regards...

eq := (1+6*(l/h)^2/(1+nu))*(diff(u(xi, tau), xi, xi, xi, xi)+int(-B*lambda*exp(-lambda(tau-s))*(diff(u(xi, s), xi, xi, xi, xi)), s = 0 .. tau))+diff(u(xi, tau), tau, tau) = alpha*(int((diff(u(xi, tau), xi))^2, xi = 0 .. 1)+int(-B*lambda*exp(-lambda(tau-s))*(int((diff(u(xi, tau), xi))^2, xi = 0 .. 1)), s = 0 .. tau))*(diff(u(xi, tau), xi, xi))+V^2*(sum(j*u(xi, tau)^(j-1), j = 1 .. 8))

jing-Fu.mw

The program below is a high school problem, related to the area a horse can graze, given it is tethered to a rectangular barn.  The level of difficulty is related to the length of rope.  

   I wanted to display some graphics of the field, barn and tethered horse - this latter being the most difficult.  I experimented with a .png picture of a plain silouhette of a horse, imported this into Photoshop, then saved it as a .pdf file, importing this into Maple,  I managed to import this into the worksheet, but I wanted a scaled down version of the horse in the program plots[display] section.  I was unsuccessful in this.  Undeterred, I decided to try and draw a version of a horse using the plots/plottools packages.  The resulting "horse" looks more like a cat, warthog,  mouse or chameleon! 

   I understand later versions of Maple are able to import graphic images.   I'd appreciate some feedback as to how easy this is, and the quality of the resulting images in Maple output.

Thanks,

    David  .  .    

restart:

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Horse tethered to barn - what area of grass?

# # # # # # # # # # # # # # # # # # # # # # # # # # # #

with(plots):

with(plottools):

macro(palegreen=COLOR(RGB, .5607, .9372, .5607)):

col1:=`black`:

print(`A horse is tethered to the corner of a barn, 10 m wide and 20 m long.  Find the area`);

print(`the horse can graze, if the length of rope is:`);

print(` i.)   5 m   ii.)  25 m  amd iii.)  50 m`);

#Length of rope

L:=10:

#Dims of barn

len:=20:wid:=10:

#Position of bottom left corner of barn

x_barn:=50:y_barn:=50:

len:=20:wid:=10:

#dimensions of field

flen:=120:fwid:=110:

rect_barn:=rectangle([x_barn,wid+y_barn], [len+x_barn,y_barn], color=brown):

rect_field:=rectangle([0,fwid], [flen,0], color=palegreen):

#Position of horse

x0:=37:y0:=32:

a := 4: b := 2.5:

belli := ellipse([x0,y0], a, b, filled=true, color=col1):

legf:=line([x0-1,y0-2], [x0-2,y0-6], color=col1, linestyle=1, thickness=1):

legf2:=line([x0-2,y0-2], [x0-3,y0-6], color=col1, linestyle=1, thickness=2):

rleg:=line([x0+1,y0-2], [x0+2,y0-6], color=col1, linestyle=1, thickness=2):

rleg2:=line([x0+2,y0-2], [x0+3,y0-6], color=col1, linestyle=1, thickness=2):

head := polygon([[x0-6,y0+3],[x0-5,y0+4], [x0-2,y0+5], [x0-3,y0+2]], color=brown, linestyle=3, thickness=2):

tail:=line([x0+6,y0-4], [x0+4,y0+1], color=col1, linestyle=1,thickness=2):

a := arc([x0+13,y0+3], 15, Pi/2..Pi+.1, color=blue):

plots[display](a,tail,head,belli,legf,legf2,rleg,rleg2,rect_barn,rect_field, scaling=constrained, axes=none);

In the link below I attempt to solve 2 trig series which are essentially equivalent as indicated by the numerical output of eq (5).  The series  represented by S13 & S14 has arguments of the trig functions that realizes that only the odd terms for k yield non-zero results.  The case represented S11 & S12 by makes no such presumption; nonetheless, all cases agree within reason numerically.  Now to find min/max values taking the derivative is needed which is simply done by removing the integral as indicated by Q1 through Q6.

Now resolving the roots works OK for Q6 because beta = 2*pi *t/T conveniently collapsed the numerator into factorable expressions.  Resolving the roots for Q3 did not work so well because what I think is that the expression in red has multiple roots so it only spits out t as the solution?  I expressed the angle alpha in terms of beta & probably need to resolve kappa to somehow get the expression in red to collapse into a factored expression, but I am not sure how to execute this.  When I solve for kappa I get ZERO.

Does anyone have suggestions?  Remember I demonstrated that both series are practically idendical numerically; hence, there derivatives should be as well as long as both series are well behaved functions.  So the solutions must be the same as well.

trig_series_solns.mw

Dear bright people of MaplePrimes, 

I'm stuck in a problem with dsolve.

I have a ODE system that I would like to solve numerically (because it's huge) in vars: var1(t), var2(t), var3(t), etc... Inside the ODE there are procedures with arguments like proc(f(x,y), a, b, c, etc...) where f(x,y) is a function for a curve (so x and y are variables) and a,b,c are numeric. 
Procedures have been written as indicated in the help page, i.e. differentiating whether the procedures are called with symbolic arguments or numeric arguments. So I call dsolve specifying the "known" procedures and a numeric method. Maple sets the problem correctly. However, when it tries to solve the equations numerically it points out that in the ODE ys there are some undefined parameters. Specifically, those parameters are x, y. But, again, x and y are not parameters but variables that are used in the procedures within the ODEs. 

I tried to include x and y as parameters and solve the system. However, before retrieving the solution, a numerical value must be given to all the parameters. 

What should I do if I need to keep f(x,y) symbolic in my procedures but I want to solve my ODE numerically? 

Thank you for supporting me. 
Thank you so much. 

Andrea



 

 

Hello,

I am trying to get Maple to display sin²(x)  rather than (sin(x))².  In particular I am trying to have it output the latex for the prior using latex(sin^2(x) , output=string), or similar.

Any ideas would be greatly appreciated.

Thanks,

Mark

To determine whether or not equilibrium points of a nonlinear ordinary differential equation is globally stable, a Lyapunov function is often employed. Since there are no general methods for constructing Lyapunov functions, May I know if there are methods in MAPLE that can be used to determine these Lyapunov functions? Thanks

Just want some input if anyone thinks this is a bug or not

Hiding the contents of equation labels in one table (table -> properties -> uncheck show equation labels) removes all reference to the labels within that table.  Is that supposed to occur?

The table below has show equation labels checked.  If I uncheck the show equation labels in the first table I would expect the reference labels (1) and (2) to disappear and (3) and (4) references in the next table to remain unchanged.

However unchecking show equation labels in the first table relabels the two equations in the second table to (1) and (2) as shown below.  Is this a bug?

However this doesn't disrupt further content in the worksheet if references were made to equation label (1). After unchecking show equation labels in the first table, all original references to label (1) are replaced with the actual value (sin(x))

I have a series with an integral inside the series.  I have worked the problem 2 different ways using sum vs Sum.  The integration variables are independent of the series variables so swapping the order of operation should not matter, but in the case, (S2), I do get a difference & I do not understand why.  The explanation fo INERT vs ACTIVE I do not think explains this.  The reason why I say this is because S1 the ACTIVE sum concurs with the INERT expressions S3 & S4.  S2 is swapping the order of operation for the ACTIVE sum does not yield the same result as the other 3 cases.  Why is this?  I am at a loss so including examples would be helpful to me.

swapping_orders_of_operation.mw

I'm a new Maple user so there may be a better way to do this, but Maple is not handling units the way I would expect.

Here is an example document (inline graphical below, also here: Plots_With_Units.mw) showing the impedance of a parallel resistor, inductor, and capacitor.  The plot is correct and it shows kHz along the abscissa like I want.  In order to get this I used kHz in the range fr, which is fine, but I had to also use kHz in the basic definition functions for Zl and Zc.

Now in order to get correct results from any of the Z functions I must use them with a kHz argument for f.  If I want to use them where other unit multipliers are more appropriate they won't work right, and many times I don't know what the appropriate multiplier should be until I'm into the design.  Then I need to go back and change the multipliers in the functions.  Or maybe in a single design I'll want to show Hz and kHz for the same function.

This seems like confusing units and dimensions.  The dimensions of inductive impedance (Zl), for example, can be expressed as frequency times inductance.  Whether the frequency is in units of Hz, kHz, or uHz doesn't matter and should simply scale the results.  I should be able to specify functions in dimensions and use units elsewhere as I want for convenient plotting and result formatting.

Is there a better way to do this, or is it a limitation in Maple?  The overall goal is to define functions with units but be able to use them and to format plots in whatever other units I like.