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"green" <rov### [at] gmail com> 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.
Post a reply to this message
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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
}
Post a reply to this message
Attachments:
Download 'rotations_in_1_2_3_axes.mp4.mpg' (3576 KB)
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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%)
Post a reply to this message
Attachments:
Download 'earth.mp4.mpg' (292 KB)
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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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clipka <ano### [at] anonymousorg> wrote:
>
> 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.
Hmm; I think the physical set-up for filimg two-axis rotation would have
presented a problem.
Having worked in the physical special-effects field -- :-) -- my initial
thought would be to build a simple 2-axis motorized rotation gimble, to hold the
asteroid model-- with a single rod attached to the 'inner' gimble for skewering
the model and holding it. (A chicken on a spit). For simplicity, think of the
inner gimble as rotation around x (in POV-Ray terms), and the outer gimble as
around z.
Depending on the camera position, the attachment rod's point of contact with the
model would be invisible most of the time (hidden by the asteroid itself.) But
eventually, that attachment point would rotate into a position that's visible to
the camera (with the rod obscuring a small part of the model, 'in front of it'
so to speak.) Having realized this problem from the get-go, I would have said
that, no, it can only rotate around one axis. Sorry, Stanley.
There's a much easier method to do this, of course: aim the camera at the
ceiling of the filming stage, and simply drop the asteroid from a good height,
past the camera. (Filming it in slow motion.) But Kubrick being Kubrick, he
would probably have given an emphatic thumbs-down to such a crude and
uncontrollable method.
Just sayin' :-D
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"Kenneth" <kdw### [at] gmailcom> wrote:
>
> ...I'm working up a 'better' example-- with a
> few new realistic constraints added. I'll post that asap.
>
Two of THESE animation examples are what my own mind's eye wants to see in
POV-Ray, for free-fall.
I actually like all three, but I like B) and C) better. The two-axis rotation
of C) *might* not be physically correct, but it looks cool anyway ;-)
The red dot represents the 'center of mass' of the object (just a guess, of
course), and the rotations are around that point. Those 'off-center' rotations
automatically make the result look more realistic, IMO.
For the two-axis rotation, it looks like the 'degree' of one or the other needs
to be constrained, possibly so that the two do not exceed a certain ratio(?).
1:1? 1:0.5? Otherwise, maybe that's when the odd 'reversed rotation' appearance
starts showing up?
For finding the *actual* center-of-mass (for a simulated POV-Ray animation
anyway), I think there might be a relatively simple scheme based on the 'reduced
mass' concept I previously mentioned. (That concept at its simplest takes two
separated masses-- like two Suns orbiting each other-- and comes up with a
single mass, the rotation point for the pair.) Even though my animated object is
a *single* object, it's made of simple separate parts. The *individual* parts
could be thought of as separate Suns (in a step-by-step fashion for the
computations?) Anyway, although a POV-Ray object has no real 'mass', that can be
simulated too (for an object made of simple geometric parts like spheres,
cylinders, etc.) Assuming that the parts are all made of the same stuff--the
same density--, the VOLUMES of the parts can be a stand-in for their separate
masses. And the volumes can be computed from the surface area(s).
So far, it's just an interesting set of ideas, that I haven't tried working out
yet.
---------------
The codes for the animation examples (a 400-frame animation):
A)
object{OBJ
rotate <-4000,0,0>*clock
rotate 360*rand(S) // arbitrary rotation
}
B)
object{OBJ
rotate 360*rand(S) // arbitrary rotation
rotate <-4000,0,0>*clock
rotate 360*rand(S) // arbitrary rotation
}
C)
object{OBJ
rotate <-4000,0,0>*clock
rotate 360*rand(S) // arbitrary rotation
rotate 800*clock*y
rotate 360*rand(S) // arbitrary rotation
}
Post a reply to this message
Attachments:
Download 'rotations_in_1_vs_2_axes_redone.mp4.mpg' (3646 KB)
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"Kenneth" <kdw### [at] gmailcom> wrote:
> my initial
> thought would be to build a simple 2-axis motorized rotation gimble...
Gimble-- That was the name of a big department store in New York City. Duh.
GIMBAL
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On 10/10/2018 17:06, Kenneth wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
>> my initial
>> thought would be to build a simple 2-axis motorized rotation gimble...
>
> Gimble-- That was the name of a big department store in New York City. Duh.
>
> GIMBAL
>
Hands up all those that noticed.
I certainly didn't.
--
Regards
Stephen
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