Maple Questions and Posts

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I am trying to solve a set of ODEs with dsolve. There are 26 equations of my ODEs, but the problem is a multiple point bvp. So the range is divided into three region. In order to use dsolve, I transform the three subregion's coordinate into 0 to 1. Meanwhile, the ODEs are different in three regions, respectively. So, there are 26×3 equations in total. And according to the paper I want to replicate, it says the response is unstable,so parameter continuation is used. Similar to the paper, an additional equation is added(eq1_27 in code), also an additional condition is added(about lambda). When the lambda is less then 0.11, the dsolve works, but for other values it doesn't work. Could anyone help me?

 

Sorry for the tedious programming code, I am new to Maple.

Hi!

I would like to write an automated code, this means that I would like not to copy and paste anything.
 

 

4.22647099771398*exp(-0.0104163888375266*t) - 4.22647099771398*exp(-2.00033505979518*t)

I have this as my last result and would like to use the value of the exponential function (0.0104163888375266 and 2.00033505979518) without having to manually copy and paste it into the next function.

How can i do this?

Thank you in advice for your help! :)

Its easy to calculate a potential function for a vectorfield 
But now by hand in 2D Input mode ..a struggle 

Doing your homework in 2D Input mode is something totally different then the structurized explanations done in Maple input for lessons by an instructor. 

Partiel differentation with respect to what variable, is not notated in 2D mode, so a serie of them showing up in the document says nothing.and reexecuting them a couple of times doubles the output if you have used a inline notation. 
Basic idea here f-> f ' -> F(f ') = f  and handling variables x,y, and z for integrating/differentation 

-----------------------------------------------------------------------


 

restart

with(Student:-VectorCalculus)

BasisFormat(true)

v := VectorField(`<,>`(x, y, z))

Vector(3, {(1) = x, (2) = y, (3) = z})

(1)

Student:-VectorCalculus:-ScalarPotential(v); "_noterminate"

(1/2)*x^2+(1/2)*y^2+(1/2)*z^2

(2)

Thats easy to use the ScalarPotential for a manual exercise

Example 2: finding a Potential function

Show that F = [exp(x)*cos(y)+y*z, x*z-exp(x)*sin(y), x*y+z] is conversative and find a potential function for it.

F := VectorField(`<,>`(exp(x)*cos(y)+y*z, x*z-exp(x)*sin(y), x*y+z))

Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z})

(3)

"(->)"

y*z*x+exp(x)*cos(y)+(1/2)*z^2

(4)

NULL

NULL

NULL

ScalarPotential(F)

y*z*x+exp(x)*cos(y)+(1/2)*z^2

(5)

So "f(x,y,z):=y z x+(e)^x cos(y)+(z^2)/2 + C :"

Now manual

'F' = value(F)

F = (Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z}))

(6)

(exp(x)*cos(y)+y*z)*`#mover(mi("e"),mo("&lowbar;"))`[x]+(x*z-exp(x)*sin(y))*`#mover(mi("e"),mo("&lowbar;"))`[y]+(x*y+z)*`#mover(mi("e"),mo("&lowbar;"))`[z]

(exp(x)*cos(y)+y*z)*`#mover(mi("e"),mo("&lowbar;"))`[x]+(x*z-exp(x)*sin(y))*`#mover(mi("e"),mo("&lowbar;"))`[y]+(x*y+z)*`#mover(mi("e"),mo("&lowbar;"))`[z]

(7)

"(->)"

F

(8)

F

Vector(3, {(1) = exp(x)*cos(y)+y*z, (2) = x*z-exp(x)*sin(y), (3) = x*y+z})

(9)

NULL

NULL

M := exp(x)*cos(y)+y*z; N := x*z-exp(x)*sin(y); P := x*y+z

x*y+z

(10)

"(->)"

x

(11)

M1 := exp(x)*cos(y)+y*z

exp(x)*cos(y)+y*z

(12)

 =

exp(x)*cos(y)+y*z

(13)

"(->)"y   ( to z )

NULLNULL 

M2 := exp(x)*cos(y)+y*z

exp(x)*cos(y)+y*z

(14)

 =

exp(x)*cos(y)+y*z

(15)

"(->)"-exp(x)*sin(y)+z (to y) NULL

N1 := x*z-exp(x)*sin(y)

x*z-exp(x)*sin(y)

(16)

 =

x*z-exp(x)*sin(y)

(17)

"(->)"x  (to z)

N2 := x*z-exp(x)*sin(y)

x*z-exp(x)*sin(y)

(18)

 =

x*z-exp(x)*sin(y)

(19)

"(->)"-exp(x)*sin(y)+z (to x)

P1 := x*y+z

x*y+z

(20)

 =

x*y+z

(21)

"(->)"x  (to y )

P2 := x*y+z

x*y+z

(22)

 =

x*y+z

(23)

"(->)"y  ( to x )

 

 

Test for to be a conservative field

P1=N1 ,  M1=P2, N2=M2

 

int(F, x).... integrating F  with respect to x ,holding  y and z fixed
Its a vector form F , probably F must be converted to scalar form? (command?)

exp(x)*cos(y)+y*z+x*z-exp(x)*sin(y)+x*y+z

exp(x)*cos(y)+y*z+x*z-exp(x)*sin(y)+x*y+z

(24)

"(->)"

x*z+(1/2)*x^2*y+(1/2)*x^2*z+y*z*x+exp(x)*cos(y)-exp(x)*sin(y)

(25)

Ok, can integrate to 3 variables now

Now the partial diretives from f

M1 = exp(x)*cos(y)+y*z"(->)"y*z*x+exp(x)*cos(y) + g(y,z) constant of integration of f (the potential function)NULL

So : "f(x,y,z)= "y*z*x+exp(x)*cos(y)NULL + g(y,z) (1) # a total mess as notation here done by me

 

The logic from this all not yet completely understood and lost oversight , but this equation (1) must be further  integrated/differentiated  to get

y*z*x+exp(x)*cos(y)+(1/2)*z^2+C

Step by step following the text example in Thomas Calculus (page 1075, example 2) in 2 D mode is not going well.

 

``


 

Download thomas_calculus-vb2-blz_1075_-vraag_forum.mw

 

Is there a way to find what changed in each Physics update? Even if it is just one or two lines short summary? I am not able to find how to do this.

For example, after doing Physics:-Version(latest); and getting a new version, how to find what was fixed/added to new version?

There is a page in help titled "Overview of the Physics Updates" but I am asking about what specific change made in each update and not as general overall description as the above page talks about.

Again, even if the changes are short, it will be nice to know what changed each time.  

 

Hi,

I can’t block the display of my p and A variables even if I finish my commands with both points.

Ideas? ThanksTrianglesQuelconques.mw

After running the program without any error, no plot obtained.

What is the reason?

Thanks3.mw

 

Hello,

I'm writing a script that solves a system of equations. I have 2 unknows that I seem to get when using "explicit" et "allvalues". The result I get from "allvalues" is in this form. My question is : how can I get just the result, without the "lambda22=" (other than copy/paste of course ;))?

lambda22 = sqrt(10)*sqrt(lambda11*(pi*lambda11 + 90))/(30*lambda11)

My code is

kappa:=30:
tensF:=Matrix([[lambda11,0,0],[0,lambda22,0],[0,0,lambda22]]):
tensFbar:=Matrix([[lambda11bar,0,0],[0,1/sqrt(lambda11bar),0],[0,0,1/sqrt(lambda11bar)]]):
tensBbar:=Multiply(tensFbar,Transpose(tensFbar)):

tensPK:=Matrix([[pi,0,0],[0,0,0],[0,0,0]]):
tensPK1:=Multiply(Transpose(MatrixInverse(tensF)),(2/Determinant(tensF))*a*(tensBbar-(1/3)*Trace(tensBbar)*Matrix(3,shape=identity))+kappa*(Determinant(tensF)-1)*Matrix(3,shape=identity)):
eq1:=tensPK[1,1]=tensPK1[1,1]:
eq2:=tensPK[2,2]=tensPK1[2,2]:
sys:={eq1,eq2}:
sol1:=solve( sys, {lambda11bar,lambda22},explicit):


allvalues(sol1[1][1]);
allvalues(sol1[1][2]);

This should be something easy to get but I don't find the method anywhere.

Many thanks in advance if you know how to do this,

Manon

Hi, 

I try using the DeepLearning package.
I use the function Classify and, even in the simplest test case presented in the its help page (please look at it), I regularly get connection errors to the mpython server as soon as I execute classifier := Classify(...) or classifier(...) more than once.
Errors are one of these twos

Error, (in Train) unable to communicate with mpython server
or
Error (in Python:-EvalFunction) unable to communicate with mpython server

I work with Windows 7 Enterprise, on an 8 proc PC and 64 GB of memory. The worst situation happened when Maple didn't even return these errors and that I saw inflating the consumed memory in 2 minutes, forcing me to manually shut down my PC because the task manager wasn't no longer  operational.

Is it a known problem?
Could it be an installation problem?


Even if it's not the point here, I would like to say that trying to use the DeepLearning package is really challenging considering the poverty of the help pages.

Natural_frequency_No_Foundation_Mass.mw

Natural_frequency_No_Foundation_Mass.pdf

Hi guys,

I am trying to determine the first 5 eigen frequencies of a bending beam with rotational and translational spring supports. This is done by setting the determinant of the coefficient matrix equal to zero. I use RootFInder -> Analytic to find the first 5 roots between 0.001 and 0.1. After I substitute the roots back in to the equation they do not give me a zero value.

Can someone see where this goes wrong?

 

Hello Everyone,

please forgive these kind of "easy" question, but I spent the last hour trying to figure out how to give the correct boundary conditions to my dsolve-function...
What I what is to create a function that says diff(f(x),x$2)(w) = 0 where f is an arbitrary function and w is an arbitrary value. Basically, it shall create the second derivative and then evaluate it at a specific point w.
I have tried the diff-function, like this: diff(f(x),x$2)(w) = 0, but this is outputting a mess. And I cannot get the D-operator to function with a second derivative and quite frankly I do not quite understand yet how it works.

So my question would be: How many I make Maple create a second derivative and evaluate it at a specific point?

Thank you and best Regards,
Lennart

Hello

Since this is my first attempt to use plots[animate], please forgive if my question is silly.  

I want to use plots[animate] with RootLocusPlot to show the effect of variable.   Here is my attempt.

num:=10*(s+alpha);den:=s*(s^2+4*s+8);
plots[animate](RootLocusPlot,[NewSystem(subs(alpha=a,num/den))],a=1..10);

Of course, when issuing the commands, an error comes out:  

Error, (in plots/animate) symbolic value(s) in model: a
 

  • Although I could define sys using NewSystem with a symbolic value, alpha, I have no idea how to assign a value for alpha.  subs(alpha=2,..) does not seem to work.
  • If I remove the square brackets in the second argument of plots[animate], a different msg comes out.  Why do I need (or not) them? 

Many thanks.

 

Equations

 

ODES := (diff(f(eta), `$`(eta, 4)))/((1-phi1)^2.5*(1-phi2)^2.5*((1-phi2)*(1-phi1+phi1*rhos1/rhosf)+phi2*rhos2/rhosf))+S*(f(eta)*(diff(f(eta), `$`(eta, 3)))-3*(diff(f(eta), `$`(eta, 2)))-eta*(diff(f(eta), `$`(eta, 3)))-(diff(f(eta), eta))*(diff(f(eta), `$`(eta, 2)))) = 0,

(khnf/kf+(4/3)*R)*(diff(theta(eta), `$`(eta, 2)))/((1-phi2)*(1-phi1+phi1*rhos1*cp1/(rhosf*cpf))+phi2*rhos2*cp2/(rhosf*cpf))+S*Pr*(f(eta)*(diff(theta(eta), eta))-eta*(diff(theta(eta), eta))-gamma*(eta^2*(diff(theta(eta), `$`(eta, 2)))-2*eta*f(eta)*(diff(theta(eta), `$`(eta, 2)))-eta*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), `$`(eta, 2))))) = 0

Boundary Conditions

 f(0) = 0, ((D^2)(f))(0) = 0, (D(theta))(0) = 0, f(1) = 0, (D(f))(1) = 0, theta(1) = 1

 

phi1 = .1, phi2 = .1, rhos1 = 2720, rhos2 = 2810, rhosf = 997.1, khnf = 1.083061737, kf = .613, cp1 = 893, cp2 = 960, cpf = 4179, Pr = 6.2, knf = .8154646474., S=0.5,R=0.5, gamma=0.5

I am tried to solve it showing following error

Error, (in dsolve/numeric/bvp) matrix is singular

 

I have got a problem with 2D plot:

I plot a x vs y(x) but now i want to plot y(x) vs x.(x should be in vertical axis)

Be an ellipse E of center O, of foci F, F1, of major axis AA1 (OA=a, OF=c), M a point of E, m its projection on AA1, T and N the points where the tangent and the normal in M cut AA1 respectively. How to establish the formulas: NF=c/a*MF; Om*OT=a² ; ON=c²/a²*Om ? Thank you.

Hi all,

There is issue with modp1(('Embed')(...)) function.

Please look at the file:

bug_embed.mw

As you can see in lines 1, 3, 5 Embed function in combining with Constant cutting several digits from argument.

Thank you.

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