Advanced Search

Rouben Rostamian

8501 Reputation

23 Badges

19 years, 37 days
Contact Rouben Rostamian

MaplePrimes Activity


These are replies submitted by Rouben Rostamian

Thanks...

Rouben Rostamian 8501
November 25 2019
0 0

@acer Thanks for confirming the issue and the very nice workaround. I had not even noticed the axis label, and I agree with you that it should not be there.

I will file an SCR.

Works in Linux...

Rouben Rostamian 8501
November 23 2019
0 0

Alt+F4 works as intended in Linux Maple 2019.2.  

Only one light...

Rouben Rostamian 8501
November 22 2019
0 0

@Christian Wolinski 

You are correct; only one light source may be specified, and that's a shame.  I pointed this out in a message not long ago.  Improved 3D lighting is high on my wish list of Maple improvements.

 

Post the data...

Rouben Rostamian 8501
November 22 2019
0 0

The inflection point of discrete data is not a well-defined concept, therefore there is no definitive answer in general.  But if the data is sufficiently "nice", then perhaps something specific to that data can be worked out.  Post your data to get useful answers.

Good...

Rouben Rostamian 8501
November 22 2019
0 0

@one man That's cool.  Thanks for the explanation.

Supplying initial conditions...

Rouben Rostamian 8501
November 21 2019
0 0

@ecterrab Thanks for pointing out this out.  I didn't know that.

I see that passing a vector/matrix to dsolve works even when boundary conditions are supplied, as in:

S := diff(Phi,t) =~ A . Phi + B;
ic := < phi[1](0)=3, phi[2](0)=5 >;

Then both of the following produce the solution of the inital value problem:
dsolve(<S, ic>);
dsolve({S, ic});

It's also possible to specify the initial condition as a sequence:

IC := phi[1](0)=3, phi[2](0)=5;
dsolve({S, IC});

 

Problem with 2019.2...

Rouben Rostamian 8501
November 19 2019
0 0

I pointed this out when 2019.2 was announced. The response was "we are investigating".  I expect a fix to come out soon. in the meantime, users should stick to 2019.1.

Something screwy...

Rouben Rostamian 8501
November 19 2019
0 0

Yes, there is something screwy with the way Maple 2019.2 handles the user initialization file and that causes all sorts of troubles.  I pointed this out when 2019.2 was announced. I expect me a fix coming out soon. In the meantime I suggest not to install 2019.2 if you haven't done so already.  Wait for the next upgrade.

 

Hollow cylinders...

Rouben Rostamian 8501
November 18 2019
0 0

@Carl Love The dynamics of a spinning object depends entirely on the relative ratios of its three principal moments of inertia.  In the calculation below I show that those ratios are not appreciably different between the hollow and solid versions at least for the particular geometry that I used in my animation.

> 

restart;

We define a T-shaped surface consisting of two intersecting hollow cylinders.
The radius of each cylinder is a.  The vertical part of the T has height h while
the horizontal part has length 2*h.  We assume throughout that h >= a.
Here is a sketch of the object.

> 

a := 1:  h := 2:
plots:-display([
  plot3d([a*cos(t), a*sin(t), z], z=a*abs(cos(t))..h, t=0..2*Pi),
  plot3d([x,a*sin(t),a*cos(t)], x=a*cos(t)..h, t=-Pi/2..Pi/2),
  plot3d([x,a*sin(t),a*cos(t)], x=-h..-a*cos(t), t=-Pi/2..Pi/2),
  plot3d([x,a*sin(t),a*cos(t)], x=-h..h, t=Pi/2..3*Pi/2)
], scaling=constrained, axes=none, style=surface,
  color=[red,"Green", "Green", blue]);
a := 'a': h := 'h':

We refer to the object through Cartesian coordinates xyz where the x and z axes
coincide with the axes of the cylinders, the zaxis being vertical and pointing up
in the configuration shown above.

We wish to calculate the location of the object's center of mass, and its principal
moments of inertia relative to the center of mass.  For that it is necessary to
integrate several functions f(x, y, z) over the object's surface.  With the help of
the constructions that led to the plot shown above, we are led to the following proc
which takes any function f = f(x, y, z) and calculates its integral over the surface.

> 

integrate_over_T := f ->
   int(f(a*cos(t),a*sin(t),z)*a, z=a*abs(cos(t))..h, t=0..2*Pi)
 + int(f(x,a*sin(t),a*cos(t))*a, x=a*cos(t)..h, t=-Pi/2..Pi/2)
 + int(f(x,a*sin(t),a*cos(t))*a, x=-h..-a*cos(t), t=-Pi/2..Pi/2)
 + int(f(x,a*sin(t),a*cos(t))*a, x=-h..h, t=Pi/2..3*Pi/2):

Here we calculate the object's surface area:

> 

A := expand(integrate_over_T((x,y,z)->1));

6*Pi*a*h-8*a^2

and its moment about the xy plane:

> 

M__xy := expand(integrate_over_T((x,y,z)->z));

a*h^2*Pi-(3/2)*a^3*Pi

The center of mass is located on the z axis due to symmetry.  The z coordinate
of the center of mass is

> 

z__g := simplify(M__xy/A);

(3*Pi*a^2-2*Pi*h^2)/(-12*Pi*h+16*a)

The principal moments of inertia relative to the center of mass are:

> 

I__x := simplify(integrate_over_T((x,y,z)-> y^2 + (z - z__g)^2));

((81*Pi^2-1792)*a^5+2784*Pi*a^4*h-1188*Pi^2*a^3*h^2+192*Pi*a^2*h^3-108*Pi^2*a*h^4)/(-216*Pi*h+288*a)

> 

I__y := simplify(integrate_over_T((x,y,z)-> (z - z__g)^2 + x^2));

((81*Pi^2-2048)*a^5+2400*Pi*a^4*h-756*Pi^2*a^3*h^2+576*Pi*a^2*h^3-396*Pi^2*a*h^4)/(-216*Pi*h+288*a)

> 

I__z := simplify(integrate_over_T((x,y,z)-> x^2 + y^2));

4*Pi*a^3*h-(56/9)*a^4+(4/3)*Pi*a*h^3

Let's consider the case a = 1, h = 5 which correspond to the dimensions of the
(solid) object in the animation shown in my earlier post.   Calculate the ratios
I__x/I__z and I__y/I__z.  The equations of dynamics depend only on these ratios,
and not on the absolute values of I__x, I__y, I__z.

> 

evalf(eval([I__x, I__y, I__z]/I__z, {a=1, h=5}));

[.4669378731, 1.313692168, 1.000000000]

For a solid object of the same dimensions the ratios are

"[0.4222514079,1.340824340,1.000000000]"

We see that the ratios of the solid and hollow objects are quite comparable,
and therefore we don't expect an appreciable difference between how they move.

 

 

Download hollow-object.mw

 

@Lali_miani As I wrote earlier, the...

Rouben Rostamian 8501
November 17 2019
0 0

@Lali_miani As I wrote earlier, the characteristic polynomial is of the fifth degree the solution to which cannot be expressed as a formula. That's not due to a Maple's shortcoming -- it's a mathematical theorem.

But since you are looking for the signs, not the values, of the eigenvalues, there is hope.  You should look up the Routh-Hurwitz Theorem which determines the signs of a polynomial's roots without calculating the solutions.

 

 

Fifth degree polynomial...

Rouben Rostamian 8501
November 17 2019
0 0

The characteristic polynomial is of the fifth degree:
LinearAlgebra:-CharacteristicPolynomial(m, lambda);
so we don't expect a solution in terms of radicals.  Is there a reason you expect an exact value?

Maple 2019.2 bug report...

Rouben Rostamian 8501
November 14 2019

Operating system: Linux

Bug report summary: Maple 2019.2 fails to load the user initialization file   ~/.mapleinit

How to reproduce

  1. Put a printing message in the initialization file. For example print("Hello Maple User");
  2. Open a new worksheet.  You should see the message "Hello Maple User".
  3. Within that worksheet do "restart;" one or more times.  You should see the message "Hello Maple User" printed each time indicating that the initialization file is being read with each restart.

That's all good.

Now instead of opening a new worksheet, open an existing (that is, a previously saved) worksheet. You will see the "Hello Maple User" as expected.  But if within that worksheet you do a restart, you won't see the "Hello Maple User" message.  The initialization is not being read!  Any definitions/settings that you may have in the initialization file are no longer accessible.

 

Explicit solution...

Rouben Rostamian 8501
November 13 2019
0 0

@Jjjones98 Okay, then an explicit solution will exist for some but not all choices of f and g.  If you specify f and g, then you can ask Maple to find explicit solutions, if there are any.

Very nice...

Rouben Rostamian 8501
November 13 2019
0 0

@Kitonum Very nice.  Vote up!

 

Concurrent...

Rouben Rostamian 8501
November 12 2019
0 0

@Carl Love The four normals are concurrent means that all four meet at the same point.

 

First 42 43 44 45 46 47 48 Last Page 44 of 99