Hi all !

I have a list of coupled ordinary differential equations 

L := [e1,e2,e3] = [diff(z(t), t, t)*m = 0, diff(x(t), t, t)*m - B*diff(y(t), t)*q = 0, diff(y(t), t, t)*m + B*diff(x(t), t)*q = 0] with unknown functions x(t),y(t),z(t).

I want to obtain the list of "normal forms" of the ode using the DEnormal function. The help page says that it is possible to use it with an operator list but none example is given. 

Thanks!

Kevin

Dear all, 

I am trying to use the Physics package to perform a simple computation about the expression of speed and acceleration in the local polar basis (Frenet). I am trying to get something like :

Define the position vector :

differentiate wrt t to get the velocity vector 

simplifying 

Similarly :

simplifying

Can anyone please help me ? Many thanks!

So I just noticed that if you want to animate something in real time, the best you can achieve is something close but not exact.

For example lets say we have a ball travelling 22 m/s over 1000 m and I want to animate that in real time. 

ball := proc(x, y) plots[pointplot]([[x, y]], color = blue, symbol = solidcircle, symbolsize = 40); end proc:
animate(ball, [22*t, 0], t = 0 .. 1000/22, frames = floor(1000/22));

frames has to be an integer value so determining how long it will take and adjusting the frames to 1 frame per second.  It requires a bit of manipulation to get it right.  Is there a better way?  I suppose boosting the frame rate and increasing the number of frames would work but then it becomes cumbersome and any large period of times would use a high number of frames and consume enormous amounts of memory. 

Hi

I found the Manipulate Equation command tool in Maple and was wondering whether it could help me rearrange my equations into giving me certain quotient? One can do it by hand, but at an exam, time saved makes a difference and one can make silly mistakes. The math rearangement is also rather trivial...

Download rearrangemanipulate.mw

Any thoughts would be greatly appreciated, thanks in advance..!

Dear all;

I have a data, I would like to save this data in a table with labeled columns and  each column contains the corresponding values.

cretae_tabl.mw

thank you for your help 

Hi

I am trying to evaluate the following, and have tried the following commands;

How do I evaluate such an expression, is there a way to get around the invalid product error in the "coded approach"? Obviously the latter doesn't work, Maple naturally needs information concerning the limits, how does one apply assumptions to this more "traditional notation"?

Any thoughts would be greatly appreaciated, thankyou in advance.

Download integratederivative.mw

In Maple, to take the exponent of a term of the form $x^a$, we can define 

    Exponent := proc(x::`^`) 

    local r; 

    r := op(2, x); 

    return(r);

    end proc:

This also works for a term of the form $Y[1,3]^{-1/3}$.

But this does not work for taking exponent of a term of the form $Y[1,3]$. How to define a function $f$ in Maple, such that $f(Y[1,3]^{a}) = a$ for any $a \in \mathbb{Q}$? Thank you very much.

I am trying to use type(sqrt(t)*Y[1, -3]*Y[2, -6], monomial) to check if an expression is a monomial. But it returns false which is not correct. How to check that an expression in Maple is a monomial? Thank you very much.

How I can change this to smooth curve

 The vertex connectivity of a graph  is the minimum number of vertices whose removal disconnects the  
  graph. With Maple, it's easy to get the connectivity of a graph, but  I can not  find a smallest vertex cut of 
the graph g by maple. 

 If a graph has some cut vertices, I see that the function ArticulationPoints seems to be able to solve.
 But for general smallest vertex cut, I don’t see a suitable function.  For example

with(GraphTheory):
G:=CompleteGraph(2,2,2,2);
DrawGraph(G);
VertexConnectivity(G)

6

This seems easy to do in Mathematica. See https://reference.wolfram.com/language/ref/FindVertexCut.html.

Plotting of a nonlinear differential equation?

I have not used Array much before. I made an array that has 3 elements, starting index is 0 and last index is 2.

I want each element in the array to be an empty list, so I can later add to it.  (since I do not know in advanced what size of list I need in each slot of the Array).

Array(0..2,[seq([],i=0..2)])

And this works in the code I am using. But the strange thing, each time I try to save the worksheet, I get Warning about saving Large calculation.

What large caclulation? The array is empty?

Even though the code is working, and I can add to each entry in the array lists OK and been using it OK, I think may be I am not doing something right.

How to correctly creat an Array from 0..N  and initialized each entry to empty list?

Maple 2021.2

Every time I open Maple it has the invitation to Login in the top right-hand corner.  I would like to sign in but have had quite a bit of trouble doing that.  I have a user name and password with Maplesoft web store and the same for MaplePrimes.  Should either of these work to log in? 

When doing

item:=x;
res:=remove(has,item,x);

Maple returns, as expected

But when item is not a single symbol, say sin(x) or diff(y(x),x), then it no longer returns ()

item:=diff(y(x),x);
res:=remove(has,item,diff(y(x),x));

It does not return () but it now returns the input itself, as if it was not removed.

Why is that, and how to make it return () also on composite expression?  I tried flatten and inplace option. Otherwise, I will have to do a special test before. 

The strange thing is that it works on 

item:=2*diff(y(x),x);
res:=remove(has,item,diff(y(x),x));

Now it returns 2 as expected. So now it did remove diff(y(x),x). But it does not remove it when it is on its own. I assume this is by design. But it is not intuitive to the user. One would expect it to work same way on removing `x` or `sin(x)` or `diff(y(x),x)`

Hello everybody. Ive got some questions. 

As the title states: Draining a shaped container from the top, and the amount of Joule it takes to do it. That is what the questions are about. 

I did make the first one, and some attempts at the sphere questions b, and c. I left them out because i want to see what you guys come up with. I think ive got the right answers, but we will see if our answers compare. :) 

The Dutch text translated: Calculate in questions a, b, and c the amount of work (joule, J) it takes to drain a tank filled with water from the top with a pump. Each question has a discription of the shape of the tank. Take for gravity g=9.81m/s^2. For water take rho=1000kg/m^3.

a.
A coneshaped tank, the topangle is down, with a height of 2.0meters and a radius of 0.5meters. 

b.
A sphere with a radius of 1.0meters.

c.
The lower half of a sphere with a radius 2.0meters. 

Greetings,

The Function. 

Download Question_for_maple_primes_8.mw