Application of MapleSim in Science and Engineering: a simulationbased approach

In this research work I show the methods of embedded components together with modeling and simulation carried out with Maple and MapleSim for the main areas of science and engineering (mathematics, physics, civil, mechanical etc); These two latest scientific softwares belonging to the company Maplesoft. Designed to be generated and used by teachers of education, as well as by university teachers and engineers; the results are highly optimal since the times saved in calculations are invested in analyzes and interpretations; among other benefits; in this way we can use our applications in the cloud since web technology supports Maple code with procedural and component syntax.

FAST_UNT_2020.pdf

kinematics_curvilinear_updated_2020.mw

Lenin AC

Ambassador of Maple

I'm fairly new to using Maple and am having a bit of a hard time calculating the following inner product. Firstly, I define the tensors (which to this end I'm not certain they are correctly defined), 

with(Physics):

Setup(mathematicalnotation=true)

Setup(coordinatesystems=spherical):

ds2 := - dt^2 + a(t)^2 /( 1-k*r^2)*dr^2 + a(t)^2*r^2*dtheta^2 + a(t)^2*r^2*sin(theta)^2*dphi^2;
Setup(coordinates = spherical, metric = ds2);

e[mu, `~nu`] = Matrix(4, {(1,1)= a(t)/sqrt(1-k*r^2), (2,2)=a(t)*r, (3,3)=a(t)*r*sin(theta), (4,4)=1}, fill=0); (15) 
Define((15))
f[`~mu`, nu] = Matrix(4, {(1,1)=sqrt(1-k*r^2)/(a(t)), (2,2)= 1/(a(t)*r), (3,3)=1/(a(t)*r*sin(theta)), (4,4)=1}, fill=0); (28)

Define((28))

Thus, I defined two mixed tensors e[mu, `~nu`] (one covariant and one contravariant index ) and f[`~mu`, nu] (one contravariant and one covariant index).

Then, I try to take the following inner product between the two mixed tensors and the Christoffel symbols of the second kind, namely,

e[nu, `~alpha`].f[`~sigma`, beta].Christoffel [`~nu`, sigma, mu];

where I used the Physics['.'] command . However, when I try taking this inner product, it returns unevaluated.

Did I define the mixed tensors incorrectly? Does it matter how you define the indices when you're gonna take the inner product? Because taking the inner product of simply e[mu, `~nu`].f[`~mu`, nu] also returns unevaluated. Also, I should mention that  e[mu, `~nu`] and f[`~mu`, nu] are inverses of each other, is there any way to define one and get the other, since, simply changing the way in which the indices are raised and lowered doesn't take the reciprocal of the components. 

Do you agree this solution given by Maple is not correct?

restart;
pde := diff(u(x,t),t)+diff(u(x,t),x)=0;
bc  := D[1](u)(0,t)=0;
ic  := u(x,0)=exp(-x^2);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming x>0,t>0;
pdetest(sol,pde)

Result of pdetest should be zero.

I think the PDE itself is not well posed (I copied it from different forum to see what Maple does with it). But still the solution clearly does not satisfy the PDE itself for x not zero. 

Maple 2019.2.1 with Physics version 573

test.mw

I am not sure why I cannot do: plot3d([f(x,y,'g(x, y)')], x=0..1,y=0..1).

And the use of single quote in Maple 2019 and 2017 are giving different results. that is, the plot (note, not plot3d) results in the attched script by Maple 2017 and 2019 are different...

Bonjour,

Comment écrire les composantes d'un vecteur contravariant avec des indices numériques ? Ce vecteur n'est pas un spacetimevector.

Par exemple : <x^1, x^2,x^3> avec cette écriture maple interprète ces indices comme des nombres et non comme des symboles

Merci pour vore retour

I do a calculation o a simple integral

      int(cosh(cos(2*t)), t = 0 .. 2*Pi)

and get the answer 0 (zero), which I know is incorrect. The cosh function of a real argument is always positive.

If I represent the cosh function as a sum of two exponentials

(1/2)*(int(cosh(cos(2*t)), t = 0 .. 2*Pi) + int(cosh(-cos(2*t)), t = 0 .. 2*Pi))

I get    

2*Pi*BesselI(0, 1)

which looks much better.

What's the matter? Why Maple yields two different results? Victor.

Hello, Probably there is a way to do this easily but I do not quickly find it within the help.

I want

rand(0..1)

to give a true! random number and not always the same number; otherwise it should be called

predefinedlist()

Seed is deprecated, not sure it would help though. So how do I go abouts?

I went to save a file in Maple and it had large amounts of calculated data. 

Maple didn't ask me if I also wanted to save that data like it usually does - it just saved it.  Saved a 13Mb worksheet that took 5 minutes to relinquish control on my laptop. 

The function evalf(  ) will encounter a critical bug when doing the following evaluation:

restart;
P1 := 1007;
P2 := 1014;
P3 := 1014.1;
evalf(P2 - P1, 2);
evalf(P3 - P1, 2);

The first evalf( ) returns a correct value, while the second one returns a wrong value.
This is really unbelievable!

hello,

How I can remove this error for dsolve equation.

Thanks

2023.mw

Download 2023.mw

how I can gain a function that it is fitting in these data in x and y and z?

please see the following figure.

this curve is a 3D diagram in three coordinates x,y and z.

Thanks

PLOTfitting.xls

Here we simulate the motion of a container with a flat bottom that can slide on a horizontal surface subject to dry friction (Coulomb friction).  Installed inside the container is an ordinary mass/spring/damper system where the mass slides horizontally.  We impart an initial velocity to the container.  That sets the mass into motion which then affects the container's motion.  Under certain conditions the container will undergo a stick-slip motion which is evident in the simulation.

This simulation very roughly approximates the motion of a partially filled bucket of water that slides on the floor when kicked.  The idea arose in a discussoin with Carl Love and mmcdara:
https://www.mapleprimes.com/posts/211677-Mass-Spring-Conveyor-Belt-And-Dry-Friction

In the animation below, the container is shown in dark color when it slides against the floor, and light color when it sticks.

Worksheet: slosh.mw

Hello people in mapleprimes,

I could modify an expression e_n_1b to simpler e_n_1e as is in attached file.
Is there any other way to change e_n_1b into e_n_1e?

Dec_22.mw

Thank you in advance.

taro

Here is an animation of a mass-spring system where the mass slides horizontally on a steadily moving conveyor belt.

The contact between the block of mass and the belt is of the dry friction kind (Coulomb's friction). Consequently the block periodically sticks to the belt and moves forward with it until the force of the stretching spring overcomes the force of friction and yanks it back, making it to slip against the belt. In the animation the block is shown in a dark color while slipping, and a light color while sticking.

The fully executed Maple worksheet can be slow to load and requires a good deal of memory. Therefore I have attached two versions which are identical in all respects except that in one of them I have removed the Maple output to make is easy to load if your computer has limitations.

Download worksheet (no Maple output) block-sliding-on-conveyor-belt-stripped.mw

Doiwnload worksheet (with Maple output) (sorry, exceeds MaplePrime's size limit)

Hello,

I have the following expression

Ve*k21*ke*x1+Ve*k21*x1^2+k12*ke^2*x1[t]+2*k12*ke*x1*x1[t]+k12*x1^2*x1[t]+k21*ke
^2*x1[t]+2*k21*ke*x1*x1[t]+k21*x1^2*x1[t]+Ve*ke*x1[t]+ke^2*x1[t,t]+2*ke*x1*x1[t
,t]+x1^2*x1[t,t]

and I want to convert it to

x1[t,t]*(x1+ke)^2+(k12+k21)*x1[t]*(x1+ke)^2+Ve*x1[t]*ke+(k21*Ve)*x1*(x1+ke)

How can I do this opperation? This is just a simple example of a more general problem I am facing. Thanks in advance for your help