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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"Kenneth" <kdw### [at] gmailcom> wrote:
>
> BTW, I made another animation example to post-- more experiments-- but it looks
> rather 'quaint' now, in light of these newer concepts.

Ah, what the heck, I'll post it anyway, just to show five various permutations
and orderings of simple <x,y,z> rotations.  There are other possible
combinations as well-- but they probably prove nothing, because  2B), 3A) and
3B) all look similar in their respective chaotic wobbles.  1) and 2)  still look
more realistic to me, as basic computer simulations-- but 2)'s rotation values
are arbitrary, when they really shouldn't be. Ditto for all the three-axis
examples.

These are all just too simplistic. So I'm working up a 'better' example-- with a
few new realistic constraints added. I'll post that asap.

The actual codes used here:
#declare S = seed(16);
1)
object{OBJ
  rotate <270*rand(S),270*rand(S),270*rand(S)> // an arbitrary pre-rotation
  rotate <2540,0,0>*clock
  rotate 270*rand(S) // to make the rotation axis arbitrary as well
  }

2A)
object{OBJ
  rotate <1210, 0, 1949>*clock
  }

2B)
object{OBJ
  rotate <270*rand(S),270*rand(S),270*rand(S)> // an arbitrary pre-rotation
  rotate <1500, 0, 0>*clock
  rotate 1937*y*clock
  rotate 270*rand(S) // to make the rotation axis arbitrary as well
  }

3A)
object{OBJ
  rotate <1210, 1512, 1949>*clock
  }

3B)
 object{OBJ
  rotate 1512*y*clock
  rotate <1210,0,1949>*clock
  }

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Attachments:
Download 'rotations_in_1_2_3_axes.mp4.mpg' (3576 KB)

On 10/07/2018 05:36 PM, Kenneth wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
>>
>> BTW, I made another animation example to post-- more experiments-- but it looks
>> rather 'quaint' now, in light of these newer concepts.
> 
> Ah, what the heck, I'll post it anyway, just to show five various permutations
> and orderings of simple <x,y,z> rotations.  There are other possible
> combinations as well-- but they probably prove nothing, because  2B), 3A) and
> 3B) all look similar in their respective chaotic wobbles.  

Mine looked a lot like yours, especially 3A, so I don't need to post
them, but I did end up with this, which *technically* has 3 rotations :)


-- 
dik
Rendered 1024 of 921600 pixels (0%)

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Attachments:
Download 'earth.mp4.mpg' (292 KB)

I think that what would be the best way to achieve a realistic rotating object
would be to do what you suggested, and write a particle system / physics engine
that would take things like mass, rotational inertia, and external forces into
account, so that the system could determine the rotations, not follow some
arbitrarily decided upon values.

That sort of inflexible set of arbitrary rules doesn't work in real life - be it
"Law" (rules) or market economics, so you're just seeing the same thing here.
You car runs itself - you just give it gas and steer it.   If you had to
manually monitor and control the fuel mixture, the sparking sequence, the valve
timing, etc, it would quickly become unmanageable.
If someone were trying to control your car remotely by a rigid set of inflexible
rules, then there wouldn't be the necessary leeway to deal with all of the
exigent circumstances that you experience and react to during even a short ride
- other drivers, squirrels, puddles, rain, fog, losing traction in snow, etc.

In the same way  - let the object "decide" what is best for it, and of course it
will look natural.


1 and 2 look natural (1 the most) because they are more in line with what you'd
expect from an object experiencing wind resistance parallel to it's direction of
motion, and so rotating around an axis perpendicular to the axis of translation.

I would do a few things if you wanted to explore this:

Define mass for the object(s) and then find the center of mass, or "reduced
mass" so that you can rotate around that point.

There should be some fairly simple equations that relate the deflection in
response to a force on a rotating object - the moment of inertia thing.

Rotation around any other axis should be a function of the rotational speed /
moment of inertia around the primary axis.
Then you can add an external force --- and this is important - in order for it
to look natural, you need to add a visual cue and time it correctly.

Look at some of the basic recommendations for making animations and adding
sound, and they will explain that even very slight changes in the timing of the
video and sound can make something look / feel very unnatural.   Your brain is
very sensitive to these cues.

So, your other examples _might_ just need some sort of visual indication of an
external force to make it look "right" - wind, a falling stream of particles...
something perpendicular to the extra axis of rotation.

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Am 06.10.2018 um 09:47 schrieb Kenneth:
>> 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...)

Yes.

> 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.

That may be because they are not actually free-falling: They are falling
in a medium of air. And though the object in its entirety is stationary
with respect to that medium, the "ends" of the object are not, and thus
are experiencing aerodynamic forces.

> 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.)

Technically, free-falling objects in an inhomogenous gravitational field
(i.e. near another body of mass) deviate slightly from the
chicken-on-a-spit pattern. But in order for this to be noticeable the
object has to be large in dimensions, and even for an object as large as
Earth the precession period is in the order of 10k years.

Also, if 2-axis rotation of asteroits were more realistic, Kubrick would
have made his special FX team work overtime to make the impossible possible.

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