On 05/10/2018 12:59, Stephen wrote:
> Changed the order of rotation to
> rotate <0, Die_Y_rot, 0>
> rotate <0, 0, Die_Z_rot>
> rotate <Die_X_rot, 0, 0>

A comparison of the above Vs rotate <Die_X_rot, Die_Y_rot, Die_Z_rot>

The blue dice uses rotate <Die_X_rot, Die_Y_rot, Die_Z_rot>


-- 

Regards
     Stephen

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On 05/10/2018 16:50, Stephen wrote:
> On 05/10/2018 12:59, Stephen wrote:
>> Changed the order of rotation to
>> rotate <0, Die_Y_rot, 0>
>> rotate <0, 0, Die_Z_rot>
>> rotate <Die_X_rot, 0, 0>
> 
> A comparison of the above Vs rotate <Die_X_rot, Die_Y_rot, Die_Z_rot>
> 
> The blue dice uses rotate <Die_X_rot, Die_Y_rot, Die_Z_rot>
> 
> 
With animation, now.



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Regards
     Stephen

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Attachments:
Download '0001-0599.mp4.mpg' (638 KB)

Am 03.10.2018 um 14:13 schrieb Kenneth:

> Going back to first principles: An object starts out as being static (that is,
> no ROTATIONS at all.) Then a force has to impinge on it to start it rotating-- a
> 'point' force for simplicity's sake. That force has a direction vector, and acts
> on the object in 3 (de-composed) vector directions, toward the center of mass.
> The magnitudes of those three vectors depend on where the force was applied on
> the surface (relative to the object's center of mass) and the angle of contact
> with the surface. If I understand the concept of 'Euler angles' correctly, those
> three force vectors can be 'simplified/combined' into just two resulting
> rotations.

No, the effect of a single force it is just a single rotation, with an
arbitrarily oriented axis.

You may have to snap out of the Euler angles picture for this. Euler
angles are good for describing "rotations" as in "transformations", but
they're of no use for properly describing "rotations" as in "continuous
motion".


To describe a realistic no-force rotation in 3D space, if you have only
Euler angles to work with, you need three angles: A changing one
describing the rotation itself, and two fixed(!) ones describing the
orientation of the rotational axis.

For a precessing motion you'd need six angles: Two fixed ones describing
the axis of precession, one changing one describing the precession
itself, another fixed one describing the tilt of the main axis in
relation to the precession axis, and another changing one describing the
main rotational motion itself. A sixth fixed angle is needed if you care
about the phase relationship between the precession and main rotation.


What you get with two changing Euler angles is a precessing motion with
a 90 degree angle between the axis of precession and the main axis, and
a fixed axis of precession (the y axis if you use `rotate <A,B,0>`).

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clipka <ano### [at] anonymousorg> wrote:
> Am 03.10.2018 um 02:34 schrieb Kenneth:
> > To take a break from my other POV-ray chores, I made a simple animated demo of
> > what an object looks like when it rotates (in POV-ray), as if free-falling under
> > gravity-- but discounting wind resistance or any other extra force. Its a
> > comparison between applying the rotations in two axes vs. three. I made the
> > animation my own purposes (to easily refer to later), but it might be of
> > interest to others as well.
>
> If free-fall without air resistance is what you want to model, you
> should use a /single/ rotation about an arbitrary axis.
>
> This is because without external forces, angular momentum is conserved,
> i.e. the axis of rotation doesn't change.
>
>
> When you combine it with a second rotation, two things can happen:
>
> (A) If both rotational axes remain stable in space and you apply the
> rotations simultaneously, the result is just a single constant rotation
> about a different axis.
>
> A real-life equivalent would be a ball set in motion by two rollers
> touching it on non-opposing points.
>
> (B) If you apply the second rotation after or before the first, the
> result is a precessing motion.
>
> A real-life equivalent would be a rotating object mounted in a gimbal,
> which in turn is also rotating.
>
>
> Thing you get if you specify a two-axis rotation in POV-Ray is (B): The
> rotation around the X axis is applied first, then the rotation around y
> is applied, effectively changing the axis around which the first
> rotation is applied.
>
> This violates conservation of angular momentum, and thus is only
> realistic when external forces are present, such as due to air
> resistance. In that context, a precessing motion would happen if the
> (asymmetric) wind resistance remained constant, which may be close to
> realistic for some comparatively symmetric objects.
>
> A rotation about a third axis adds yet another layer of complexity,
> turning the precessing motion into a tumbling motion. This should be the
> closest to realism at least for highly asymmetric objects.
>
> In either case - precessing or tumbling motion - the motion will only be
> a rough approximation of real physical behaviour.

interesting reading on this topic
https://en.wikipedia.org/wiki/Poinsot's_ellipsoid

you can search youtube with that term.

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clipka <ano### [at] anonymousorg> wrote:

>
> If free-fall without air resistance is what you want to model, you
> should use a /single/ rotation about an arbitrary axis.
>
> This is because without external forces, angular momentum is conserved,
> i.e. the axis of rotation doesn't change.

So an analogy would be a chicken on a spit, roasting over an open fire while the
single rod is rotated? (I must be hungry at the moment...)

If we're on the same wavelength, that goes against what I *think* my eyes see
when, for example, the ISS astronauts have some playful fun by spinning
weightless objects for the camera. It looks like two-axis (POV-Ray) rotation to
me. But that's only my recollection; I need to take another look at some of
those videos. (BTW-- 2001:A SPACE ODYSSEY recently celebrated its 50th
anniversary, and there are some space shots that have asteroids tumbling near
the Discovery. I always thought they looked a bit fake-- because they are
spinning around only one axis. Granted, Stanley Kubrick spared no expense in
getting scientific details right; but my opinion is that the spinning of the
asteroids (as special-effects models) had to be constrained, simply as a
practical matter for filming. A chicken on a spit, in other words.)
>
>
> A rotation about a third axis adds yet another layer of complexity,
> turning the precessing motion into a tumbling motion. This should be the
> closest to realism at least for highly asymmetric objects.

To me, the 3-axis rotation looks not so much like tumbling, but rather like the
object has a 'shifting mass' inside it, kind of sloshing around. It's the
'changing/reversing' of directions that seems odd. (Multiple precessions?) Yet,
it DOES appear to be a good stand-in for chaotic air-resistance.

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clipka <ano### [at] anonymousorg> wrote:

>
> No, the effect of a single force it is just a single rotation, with an
> arbitrarily oriented axis.
>
> You may have to snap out of the Euler angles picture for this. Euler
> angles are good for describing "rotations" as in "transformations", but
> they're of no use for properly describing "rotations" as in "continuous
> motion".
>

Hmm.
You may be onto something there, after all. Before I become TOO stubborn and set
in my ways, I'll try... a single rotation axis. So, my *latest* POV-Ray
animation theory would then be:

1) Make an oddly-shaped object (not just a cube or cylinder). The Stanford
Bunny? A giant chicken?

2) PRE-apply a random/arbitrary rotation to the object-- just once, prior to the
animation-- to mix things up a bit

3) choose another arbitrary axis for the animation, and let it spin.

(I did neither 2) nor 3) for my posted animation.)

I'll give that a go, to see what happens.

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"Kenneth" <kdw### [at] gmailcom> wrote:
>
> So, my *latest* POV-Ray animation theory would then be:
>
> 1) Make an oddly-shaped object (not just a cube or cylinder).
>
> 2) PRE-apply a random/arbitrary rotation to the object-- just once, prior
> to the animation-- to mix things up a bit
>
> 3) choose another arbitrary axis for the animation, and let it spin

Here are the new animation results (vs. the same two-axis rotation scheme I used
in my previous animation.)

Values used...
For the SINGLE-axis version:
object{OBJ
  rotate <270*rand(S),270*rand(S),270*rand(S)> // an arbitrary pre-rotation
  rotate <2540*clock,0,0> // one axis
  rotate 270*rand(S) // // to make the rotation axis arbitrary as well
  }

For the TWO-axes:
object{OBJ
  rotate <1210*clock,0,1950*clock>
  }

I'm still eyeing the results (vs. my 'expectations'), so I'll withold judgement
for now. I need to sleep on it ;-)

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Attachments:
Download 'rotations_in_1_vs_2_axes.mp4.mpg' (3753 KB)

On 05/10/2018 00:46, Kenneth wrote:
> Stephen <mca### [at] aolcom> wrote:
> 
>> Ah! you spotted the deliberate mistake. Oops! :-(
> 
> Oh, so you're trying to play tricks on the poor gringo, eh? I'm onto ya!  :-P
> 
>> Unfortunately I have had a series of family medical problems
>> ending last month with my wife having vertigo and falling and breaking
>> her hip.
> 
> Sorry to hear that; I certainly hope the doctors can repair it (or replace the
> worn parts.) I can't even begin to imagine the pain she must have experienced.
> 

Thanks Thomas, I will pass your wishes on.
The hip seems to be healing well. The doctors are more concerned with 
the vertigo she is experiencing and the pain from her Trigeminal 
Neuralgia is stopping her from doing as much exercise as she needs. She 
is probably in the best place at the moment. It is just taking too long, 
for our liking.

-- 

Regards
     Stephen

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"green" <rov### [at] gmailcom> wrote:

> interesting reading on this topic
> https://en.wikipedia.org/wiki/Poinsot's_ellipsoid
>

That's new to me-- and indeed it IS interesting. Especially the section titled
"Special Case":

"In the general case of rotation of an unsymmetric body, which has different
values of the moment of inertia about the three principal axes, the rotational
motion can be quite complex unless the body is rotating around a principal axis.
As described in the 'tennis racket' theorem, rotation of an object around its
first or third principal axis is stable, while rotation around its second
principal axis (or intermediate axis) is not."

And,
"One of the applications of Poinsot's construction is in visualizing the
rotation of a spacecraft in orbit." (!) Or more generally, a free-falling
object.

Clipka's detailed comments are beginning to make sense to me now.

I've also come across the concept of 'reduced mass'...
https://en.wikipedia.org/wiki/Reduced_mass
..... mainly the part about "Moment of inertia of two point masses in a line."
That may seem to be tangential to the discussion here, but it helped me.

I already see that my notions of free-fall rotation have been rather simplistic,
especially regarding my attempts to mimic the movements using ONLY the simple
notion of rotate <...>, without taking ANYTHING else into account. There are
many things to consider-- an important one being 'symmetric' objects vs.
non-symmetric ones (relating to the location of their centers of mass-- i.e.,
where they should rotate from.) I guess you could say that my own 'expectation'
of ALL free-fall movement has been that of a spinning tennis racket! (Or,
another example: A gymnist doing a whirling dismount from a cross beam or
'horse'.) But not every object is like that, and a 'generic' set of rotations
may not fit every situation.

Much food for thought. Thanks for the nudge! Also thanks to Clipka and Le
Forgeron for their input; the concepts are 'deep', but I'm slowly catching on
;-)

BTW, I made another animation example to post-- more experiments-- but it looks
rather 'quaint' now, in light of these newer concepts.

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The "Tennis Racket" theorem-- it's all there! Take a look (especially at the
video clip made by a Russian cosmonaut in 1985-- the effect is named after him).
The video looks kind of like my 3-axis rotation example-- but even more weird!
Yet it's real. If one of my own animations had turned out that way, I would have
said it was *completely* unrealistic.

https://en.wikipedia.org/wiki/Tennis_racket_theorem

I also came across this ACM paper-- well, the link anyway. (Not free,
unfortunately; I haven't read it.)

ACM (Association for Computing Machinery)
"Free-fall motion synthesis" 2011
https://dl.acm.org/citation.cfm?id=2077386

My own 'practical' notion about all of this stuff-- so far-- is basically this:
It seems that rotation in two axes actually dampens out or eliminates rotation
around the third axis, for physical reasons (angular momentum, etc etc)...
perhaps depending on the degree of the initial rotation(s). And it may not be
proper or realistic to stuff just ANY values into rotate <x,y,z> (which is only
a 'stand-in' for the real physical processes anyway.) In the real world, the
values appear to be interdependent.

It's all quite complex, and I'm STILL learning...

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