Maple Questions and Posts

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Hi Users!

Hope you all are fine here. I want to draw a graphs like this

Here 

y(x)=21.70160211*x^2-35.93499295*x+19.00000000;

and 

y(x-0.8)=21.70160211*(x-.8)^2-35.93499295*x+47.74799436

Please help me how to make this for x when y(x) on x-axis and y(x-0.8) on y-axis. I am waiting your positive response. 

Thanks

 

I computed A and B matrices, now I want to write it in state space reperentation.

diff(x(t), t) = A*x(t)+B*u

where

diff(x(t), t) = (Vector(6, {(1) = diff(alpha(t), t), (2) = diff(alpha(t), t, t), (3) = diff(y(t), t), (4) = diff(y(t), t, t), (5) = diff(theta(t), t), (6) = diff(theta(t), t, t)}))

So I calculated A*x(t)+B*u and got this:

(Vector(6, {(1) = diff(alpha(t), t), (2) = diff(alpha(t), t, t), (3) = diff(y(t), t), (4) = diff(y(t), t, t), (5) = diff(theta(t), t), (6) = diff(theta(t), t, t)})) = (Vector(6, {(1) = 0, (2) = k/(J*R), (3) = 0, (4) = k/(M*R*r), (5) = 0, (6) = -k/(M*R*r*l)})).e+(Vector(6, {(1) = diff(alpha(t), t), (2) = -k^2*(diff(alpha(t), t))/(J*R), (3) = diff(y(t), t), (4) = -k^2*(diff(y(t), t))/(M*R*r^2)-m*g*theta(t)/M, (5) = diff(theta(t), t), (6) = k^2*(diff(y(t), t))/(M*R*r^2*l)+(M+m)*g*theta(t)/(M*l)}))

where u=e but the formation is not A*x(t)+B*u anymore. How can I enforce Maple to output the result in the form of A*x(t)+B*u?

‏‏‏‏I want to solve partial differential equation by adomian decomposition method, I have a mistake  in define the nonlinear term, then  the calculations of integral does not display , can anyone help me please

‏‏ADM_1.mw

I get this message everytime I am trying to open my worksheet: "Recover Corrupt File and Save As"

2.G_anden_aflevering.mw

 

Is it possible to save table settings (and set a new default), so I dont have to manually change the "indent" number in every table i make in a document?

 

Its not possible to save the settings in the table menu itself, and there is no "table" option under preferences.

Almost Happy maple user on macbook pro 18

 

I want to solve system of nonlinear ordinary differential equations numerically using the variational finite
element method (FEM). is it possible to solve on Maple? If anybody have a idea please share with me. I attach the image of my problem which I am tryimng to solve.

1) start cmaple.exe;

2) type "proc(x, x);", and watch Maple die;

3) Request a refund from Maplesoft.

Hello all,

I am presenting some results in a small meeting tomorrow and I have a rather large symbollic matrix that I was hoping to be able to view in a more readable form (once you see my code, you will see what I mean). This should be a simple fix. Furthermore, when I use the Latex command to recieve code to import into latex, its not working properly, which makes me think I made some kind of mistake. I am really just trying to get this matrix in its full for so that it is easy for other people to read. Thanks for any help.Turns_Latex.mw
 

restart

with(LinearAlgebra)``

A := Matrix(5, 5, [0, 0, 0, 0, 0, -AXX*UU-AXY*VV-AXZ*WW, AXX, AXY, AXZ, 0, -AXY*UU-AYY*VV-AYZ*WW, AXY, AYY, AYZ, 0, -AXZ*UU-AYZ*VV-AZZ*WW, AXZ, AYZ, AZZ, 0, -AXX*UU*UU-AYY*VV*VV-AZZ*WW*WW-(AXY*UU*VV+AXZ*UU*WW+AYZ*VV*WW)*2+(-E+2*UVW)*AE, -AE*UU-VL2, -AE*VV-VL3, -AE*WW-VL4, AE])

A := subs(VL2 = -AXX*UU-AXY*VV-AXZ*WW, VL3 = -AXY*UU-AYY*VV-AYZ*WW, VL4 = -AXZ*UU-AYZ*VV-AZZ*WW, A)

A := subs(AXX = mu*(zeta__x^2+zeta__y^2+zeta__z^2+(1/3)*`#msup(mi("\`zeta__x\`"),mn("2"))`), AYY = mu*(`ζ__x`^2+`ζ__y`^2+`ζ__z`^2+(1/3)*`#msup(mi("\`ζ__y\`"),mn("2"))`), AZZ = mu*(`ζ__x`^2+`ζ__y`^2+`ζ__z`^2+(1/3)*`#msup(mi("\`ζ__z\`"),mn("2"))`), A)

A := subs(AXY = (1/3)*mu*zeta__x*zeta__y, AXZ = (1/3)*mu*zeta__x*zeta__z, AYZ = (1/3)*mu*zeta__y*zeta__z, A)

A := subs(UU = u, VV = v, WW = w, A)

A := subs(AE = mu*gamma*(`ζ__x`^2+`ζ__y`^2+`ζ__z`^2)/Pr, A)

Matrix(%id = 18446744078321522678)

(1)

latex(A)

 \left[ \begin {array}{ccccc} 0&0&0&0&0\\ \noalign{\medskip}-\mu\,
 \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt
\#msup(mi("zeta}}_{\mbox {{\tt x"),mn("2"))}}}/3 \right) u-1/3\,\mu\,
\zeta_{x}\,\zeta_{y}\,v-1/3\,\mu\,\zeta_{x}\,\zeta_{z}\,w&\mu\,
 \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt
\#msup(mi("zeta}}_{\mbox {{\tt x"),mn("2"))}}}/3 \right) &1/3\,\mu\,
\zeta_{x}\,\zeta_{y}&1/3\,\mu\,\zeta_{x}\,\zeta_{z}&0
\\ \noalign{\medskip}-1/3\,\mu\,\zeta_{x}\,\zeta_{y}\,u-\mu\, \left( {
\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt
\#msup(mi("zeta}}_{\mbox {{\tt y"),mn("2"))}}}/3 \right) v-1/3\,\mu\,
\zeta_{y}\,\zeta_{z}\,w&1/3\,\mu\,\zeta_{x}\,\zeta_{y}&\mu\, \left( {
\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt
\#msup(mi("zeta}}_{\mbox {{\tt y"),mn("2"))}}}/3 \right) &1/3\,\mu\,
\zeta_{y}\,\zeta_{z}&0\\ \noalign{\medskip}-1/3\,\mu\,\zeta_{x}\,\zeta
_{z}\,u-1/3\,\mu\,\zeta_{y}\,\zeta_{z}\,v-\mu\, \left( {\zeta_{x}}^{2}
+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{\mbox
{{\tt z"),mn("2"))}}}/3 \right) w&1/3\,\mu\,\zeta_{x}\,\zeta_{z}&1/3\,
\mu\,\zeta_{y}\,\zeta_{z}&\mu\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}
+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{\mbox {{\tt
z"),mn("2"))}}}/3 \right) &0\\ \noalign{\medskip}-\mu\, \left( {\zeta_
{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}
_{\mbox {{\tt x"),mn("2"))}}}/3 \right) {u}^{2}-\mu\, \left( {\zeta_{x
}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{
\mbox {{\tt y"),mn("2"))}}}/3 \right) {v}^{2}-\mu\, \left( {\zeta_{x}}
^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{
\mbox {{\tt z"),mn("2"))}}}/3 \right) {w}^{2}-2/3\,\mu\,\zeta_{x}\,
\zeta_{y}\,uv-2/3\,\mu\,\zeta_{x}\,\zeta_{z}\,uw-2/3\,\mu\,\zeta_{y}\,
\zeta_{z}\,vw+{\frac { \left( -E+2\,{\it UVW} \right) \mu\,\gamma\,
 \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2} \right) }{\Pr}
}&-{\frac {\mu\,\gamma\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta
_{z}}^{2} \right) u}{\Pr}}+\mu\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2
}+{\zeta_{z}}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{\mbox {{\tt
x"),mn("2"))}}}/3 \right) u+1/3\,\mu\,\zeta_{x}\,\zeta_{y}\,v+1/3\,\mu
\,\zeta_{x}\,\zeta_{z}\,w&-{\frac {\mu\,\gamma\, \left( {\zeta_{x}}^{2
}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2} \right) v}{\Pr}}+1/3\,\mu\,\zeta_{x}
\,\zeta_{y}\,u+\mu\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}
}^{2}+\mbox {{\tt \#msup(mi("zeta}}_{\mbox {{\tt y"),mn("2"))}}}/3
 \right) v+1/3\,\mu\,\zeta_{y}\,\zeta_{z}\,w&-{\frac {\mu\,\gamma\,
 \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2} \right) w}{\Pr
}}+1/3\,\mu\,\zeta_{x}\,\zeta_{z}\,u+1/3\,\mu\,\zeta_{y}\,\zeta_{z}\,v
+\mu\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}+\mbox {{
\tt \#msup(mi("zeta}}_{\mbox {{\tt z"),mn("2"))}}}/3 \right) w&{\frac
{\mu\,\gamma\, \left( {\zeta_{x}}^{2}+{\zeta_{y}}^{2}+{\zeta_{z}}^{2}
 \right) }{\Pr}}\end {array} \right]

 

``


 

Download Turns_Latex.mwTurns_Latex.mw

 

Dear Sir

There is error appears when we solve system of differential equations contains 13 equations ,

the form of error

Error, (in DEtools/convertsys) invalid terms in sum: -9*Y[8]+2 .. Y[3]+.3*Y[6]+.4*Y[7]+3.5*Y[11]+3.5*Y[13]

 

Hint we use dsolve, numerically

How to overcome on this error 

 

Thanks

after i tryrring to instell another vergion of maple and it failed when i reinstell the older vergion of maple i get this error 
what is missing and i did wronge 

l := (n+m+sum(a[i], i = 1 .. n)+sum(b[j], j = 1 .. m))*ln(alpha)+n*ln(lambda[1])+m*ln(lambda[2])+lambda[1]*(sum(x[i], i = 1 .. n))+lambda[2]*(sum(y[j], j = 1 .. m))-(sum((2+a[i])*ln(exp(lambda[1]*x[i])-1+alpha), i = 1 .. n))-(sum((2+b[j])*ln(exp(lambda[2]*y[j])-1+alpha), j = 1 .. m));

Error, (in property/ConvertProperty) invalid input: PropRange uses a 2nd argument, b, which is missing


 

 

Even and odd complement each other

how to find other sequence which complement each other?

such as 3 sequences divided integers or 5 sequences divided whole integers

is there monomials creation method such that solve result about coefficient and power are integers when right side columns are sequences?

 

i find even multiplication numbers are always solved into integers coefficient and power.

is there any more other sequences?

if I choose six multiplication table sequence, 

what is this complement of six multiplication table sequence?

How do i change keyboard shortcuts, E.g one of my keyboard keys are broken or have stopped working. How do i redirect my shortcut to another keyboard combination or another hotkey simply.

Hello, is it possible to have a document synchronized in the same way as Onenote? We're a group of engieneer students wanting to share documents, however the only way we can figure out a way to do it. Is uploading to maplecloud groups, sharing a "base" document, and everytime someone "updates" the document you save a new one. So it kind of defeats the purpose of making it a smart idea of collaborating on one document, am i missing something or is this really how oldschool it works?

I was wondering how Maple cope with piecewise functions during forward integration and if it's preferable to use dsolve events option in place of defining a piecewise discontinuos function.

As far as I understood dsolve/events halts the integration each time an event is triggered and subsequently restarts the integration using the pre-trigger outputs as new initial conditions. I suppose that by using a piecewise, if a discontinuity is detected, dsolve proceeds exactly in the same way halting and restarting the integration.

Here a toy example of a 2D rolling dice (idea of a rolling dice from the rolling cube by @one man :P ) in which the reaction forces of the floor can be seen as function of the compenetration dice/ground

Both the appraches (events and piecewise) give the same results

falling_dice.mw

Hi

In mathematics, the inverse problem for Lagrangian mechanics (Helmholtz inverse problem) is the problem of determining whether a given system of ordinary differential equations can arise as the Euler–Lagrange equations for some Lagrangian function. 

For more information read section IV.2. page 65 of the following reference:

http://www.unilim.fr/pages_perso/loic.bourdin/Documents/bourdin-thesis2013.pdf

________________________________________________________________________

 

I need some hints or procedures (if it is possible) for similar (but a little more complex) problem:

1- Assume that you have one ordinary differential equation, ode1(r) in polar coordinate system (i.e. (r, theta)). The ODE is taken to be independent from theta (It is not a PDE).

2- Assume that "Euler" is an operator that gives the Euler-Lagrange equation, I need a procedure to calculate ode2(r) such that

1/(2r)*Euler (ode2(r)) -Laplacian (1/(2r)*Euler(ode1(r)))=0

It is obvious that we need inverse of Euler operator (say IE) to calculate ode2(r).

ode2(r) =IE( 2r*Laplacian (1/(2r)*Euler(ode1(r))))

I calculate ode2(r) for some simpler cases via trial and error method.

s := proc (S) 
subs(w = w(r), w1 = diff(w(r), r), w2 = diff(w(r), r$2), S) 
end proc: 
Euler := proc (f) 
s(diff(f, w))-(diff(s(diff(f, w1)), r))+diff(s(diff(f, w2)), r$2) 
end proc:

Example:

ode1(r) = -r*(diff(w(r),r))^2:

ode2(r) = (diff(w(r),r))^2/r+r*(diff(w(r),r$2))^2:

-1/(2*r)*Euler(w1^2*r):

simplify(1/(2*r)*Euler(w1^2/r+r*w2^2)-VectorCalculus:-Laplacian(%,('polar')[r,theta]))

I will be grateful if you can hint me to write an appropriate procedure.

Thanks

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