## coupled partial differential equations...

Asked by:

Hello,

I have a problem with PDE coupled that I don't know how to solve in the maple.

Are there some analitical/numerical methods to solve the problem?

Any help will be usefull!!

## Use of add or sum commands with the LieAlgebras pa...

Asked by:

Hi,

The evalDG command included in the LieAlgebras via the DifferentialGeometry package allows summations such as evalDG(e1+e2) where e1 and e2 are two generators of a given Lie algebra.

Now, let L be a list of such summations, e.g.,

L= [e1+a*e3,2*e2+b*e4,e1+3*e5]

where a and b are symbols for variable names in the real domain.
Then, while the code

evalDG(add(eval(cat(e,i)),i=1..n));

works fine (n be a given integer), the code

evalDG(add(eval(L[i]),i=1..n));

does not, and an error message results due to an "invalid subscript selector".

What is the right code to realize this summation?

Thanks.

Jaqr

## How to plot and optimize a piecewise function?...

Asked by:

Hi everybody,

This is my code:

assume(0 < a, 0 < L, a < L);

M := piecewise(0 <= x and x < a, P*x*(L-a)/L, a <= x and x < L, P*a*(L-x)/L);
ode := diff(y(x), $(x, 2)) = M/(E*I__0); ic := y(0) = 0, y(L) = 0; sol := factor(dsolve([ode, ic], y(x))); assign(sol); y1 := y(x); I have two questions: 1) How to plot y1? I would like to plot y1, but in the plot can to specify a values of a, L, P, E and I. 2) How can I find a maximun and minimun value of y1? I tried to use maximize and minimize commands but really I don't know if I used them correctly. Thank you. ## How can I solve this differential equation with in... Asked by: Hi, my problem is the next differential equation: In maple. I used this code to solved it, but throws this error: dsolve({diff(y(x), x, x) = -P*x/(I*E), eval(y(x), x = L) = 0, eval((D(y))(x), x = L) = 0}); Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(L), y(x)} What is the problem with my code? How can solve my ODE with tis boundary conditions? ## Combining arrays... Asked by: Hello. I have the equations written into the arrays. I want to combine them into a common system and solve it. I gave a simple example of what I need. How do I perform this operation?  >  >  (1)  >  (2)  >  > Download 4.mw ## how to place the calculated elements in a matrix ?... Asked by: restart; with(Student[LinearAlgebra]); A := Matrix([[2, 3, -4], [0, -4, 2], [1, -1, 5]]); for i to 3 do for j to 3 do print((-1)^(i+j)*Minor(A, i, j)) end do end do; How to code to get that is egal to Adjoint(A)? Thank you. ## How to find the maximal value of an angle ?... Asked by: An ellipse of focus F1 and F2 is considered in which the focal length F1F2=2c is equal to the length 2b of the short axis; the length of the long axis is 2a. M being any point of this ellipse, calculate the lengths MF1=x and MF2=y according to a and angle F1MF2 = alpha. What is the maximum value of alpha? Thank you for your help. ## How to write Explore command ?... Asked by: I want to vary t from -15 to -7 and from 7 to 15 how to write the Explore command? example : Explore(Fig(t), t=-15..-7 and t=7..15); which does't work. Thank you. ## solve non-linear differential equation... Asked by: Hi guys I want to solve the following non-linear differential equation but by using dsolve(), the computer cannot solve it, so please guide me. Q:=2*diff(a(t), t, t)*a(t)^3 - 3*diff(a(t), t)^4 + diff(a(t), t)^2*a(t)^2 with the best regards ## How to correct this error ?... Asked by: eqell := expand((x+(1/2)*R1-(1/2)*R)^2/a^2+y^2/b^2-1); geometry:-ellipse(ell, eqell, [x, y]); detail(ell); ellipse: hint: unable to determine if 1/(1/2*R+1/2*R1)^2*(1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R^2+2/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1*R+1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1^2) is zero Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse. How to manage this error ? Thank you. ## How do I define an orthonormal tetrad of my choice... Asked by: Hello, I want to define an orthonormal tetrad basis of my choice in a spacetime having a metric given in some system of coordinates. My problem is that Maple automatically proposes an orthonormal metric but this is not the one that suits my requirements. So, I would like to specify the tetrad basis manually. As an example, I am trying to reproduce the calculations in sections 6 and 7 of the article https://arxiv.org/abs/gr-qc/0510083 . Here, the metric$g$is given by the line element$ds^2 = - (c(t,r)^2 - v(t,r)^2) dt^2 + 2 v(t,r) dr dt + dr^2 + r^2 (d\theta^2 + sin(\theta)^2 d\phi^2)$in$(t, r, \theta, \phi)$coordinates. My chosen signature is (- + + +). Let, us adopt the convention used by Maple and denote spacetime indices by Greek alphabets and tetrad indices by lowercase Latin letters. Now, I would like to define a tetrad$e_a = (V, S, \Theta, \Phi)$(as in section 7 of the article referred to above) where: V^\mu = \frac{1}{c\sqrt{1-\beta(t,r)^2}}[1, - (v + c \beta), 0, 0] \\ S^\mu = \frac{1}{c\sqrt{1-\beta^2}}[-\beta, c + v \beta, 0, 0] \\ \Theta^\mu = [0,0,1,0] \Phi^\mu = [0,0,0,1]. Here,$|\beta(t,r)| < 1$. I do not know how I may specify this in my worksheet. This may come of use somewhere later. Now, with this choice of the tetrad, we know that$g(e_a, e_b) = \eta_{ab}$with$\eta$being the Minkowski metric in spherical coordinates. After defining this tetrad basis, I finally want to calculate Einstein tensor, components of energy-momentum tensr etc. I have problem with constructing this orthonormal tetrad basis myself. It would be great if you could help me with this. An additional curiosity: when we work with multiple tetrad bases, is it possible to denote the the tetrad indices by hatted tetrad labels themselves, as in$\eta_{\hat V, \hat \Theta}\$?

Thank you.

 > restart
 >
 (1)
 >
 (2)
 > Setup(g_=-(c(t,r)^2 - v(t,r)^2)*dt^2 + 2*v(t,r)*dt*dr + dr^2 + r^2*dtheta^2 + r^2*sin(theta)^2*dphi^2)
 (3)
 >
 (4)
 > with(Tetrads)
 (5)
 >
 (6)
 >

Download dynBH.mw

## Finding the zero roots of an equation...

Asked by:

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?

## Property of an ellipse...

Asked by:
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.

## Old problem with an ellipse...

Asked by:

A triangle ABC with fixed B and C vertex is considered in the plane, A being variable so that b+c remains constant and equal to a given length L.
We call P, T, T' the points of contact of the exinscrit circle in the angle B with the sides BC, AB and AC respectively.
Show that P is fixed and is one of the vertex of the ellipse described by point A. What are the locus of T and T'? How to animate the drawing when A move ? Thank you.

## Propriety of an ellipse...

Asked by:

In the plane, an ABC triangle is considered for the vertices B and C are fixed, A being variable so that b +c remains constant and equal to a given length l. (b=distance(A,C), (c=distance(A,B)
How to show that the product tan(B/2=*tan(C/2) remains constant ?

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