Spontaneous synchronization:
Physics, never ceases to amaze people
Also physics: I am not stable along this axis so i will just randomly skip along;
Intermediate axis theorem:
Also physics, Your axis is not same as one, i will just rotate along that perpendicular axis and surprise you;
what we mainly owe helicopter maneuvers to: conservation of momentum
I knew the third one and applied that, not to great extends but it has a good use in floating offshore wind turbines, yet it still amazes meNone of this surprises me heh....having worked with harmonics and resonances a lot.
The last lecture when he brings up stellar collapse at the end as special poignant point to angular momentum conservation was very well done.
There is of course another branch of physics also playing out here given the vastly higher energy density present at nuclear level that sustains the star for most of its lifetime. There is very small associated mass conversation all things considered compared to the full on harnessing of that mass during the collapse episode.
This also bears some carryover to exactly how neutron stars and blackholes "hold" residual energy from that collapse (that is not emitted during the nova or supernova)...in that their very physics at the nuclear level change drastically to accommodate this compared to what can exist in a more conventional physics model.
I knew the third one and applied that, not to great extends but it has a good use in floating offshore wind turbines, yet it still amazes me
The second one has emerged at some place, i wasn't acquainted with it and it took a while to find out the source is related to intermediate axis theorem,
The first one, i was surprised despite of being involved in vibration in all levels, observed it at an experiment and couldn't find the cause even if we checked damping at the system (was stable). the system was slowly being synced despite of the individual bodies were not coupled, except of the hydrodynamic coupling due to free-surface between them, well if i haven't watched those videos on YouTube probably i would never find the cause.
At the moment i know the cause but our solution was to skip that angle which triggers synchronization, and interpolate it from the nearest known angles. What is strange it doesn't appear in nonlinear simulations with similar boundary conditions and the same scale.
We know the system is stable at that angle and the individual parts do not sync, the phenomena just emerges when system is scaled down and placed into test basin
Seen it already, and i was never surprised to see those nonlinear terms are the convicts of the synchronization.Can have a read here coming back to the metronome stuff:
http://www.math.pitt.edu/~bard/classes/mth3380/syncpapers/metronome.pdf
Well i am glad to see another example in macro scale. Thanks for the information and the math.Heh, well when you go out ice skating and pull your arms in when spinning, you can pirouette helluva fast if you dont watch out.
Hehe, it actually reminded me of a professor I once had when we worked on a satellite design project. One of my louder-brash project-mates kept venturing that we needed to make the reaction wheels bigger and beefier etc...and my prof finally got annoyed with him and just said "uhhh NO, you just make them able to spin FASTER!...SILLY!" ....i.e please recognise what is linear vs squared in the angular momentum rotational stability etc.
Basically getting something to spin incredibly fast relative to its mass, is perfect way to illustrate this like in that clip you posted. With little net gravity field, you can see principal axi easily when you simply impart the high rotational intensity...in effect the reverse of what reaction wheels do.
So true, it is kind of counter intuitive at first glance, but there is sufficient transmission of the harmonics given each metronome concentrated harmonic w.r.t the system connecting them (in this case a plank on some cans, thus allowing fairly unconstrained energy interaction among a low population of items).
This is a more wide ranging phenomenon in the macro scale too...if you look at Resonant interactions at large, with the studies and works of poincare, hamilton, lagrange, fourier etc.
Take orbital resonances for example:
Looking at just Io and Europa for example (Any example will do, incl the planets themselves around the sun):
Shortest distance found between these two bodies (Io and Europa) in their respective orbits is roughly 250,000 km. At this point in time, they exert (due to their masses) about 4.5 *10^18 N on each other using Gmm/r^2.
If we look at Io, we find its centripetal force (mv^2 / R) due to jupiter is about 4.5X10^22 N.
So basically the latter is magnitude of 4 higher (10,000 times higher).
So a 0.01% relative force interaction (applied with enough consistency and time) is enough to achieve massive resonance lock.
(I did the numbers w.r.t distances, velocities and masses really quick without dbl checking so there is potentially an error somewhere , but the concept holds in general given magnitudes here I have explored before, trust me )
Can have a read here coming back to the metronome stuff:
Coincidentally in that paper (given I just brought astronomy into the picture), Huygens (who was first to discover a moon of Saturn i.e Titan) was fascinated by the "ring of saturn", which are now known to be Rings and have a number of interesting resonant phenomenon given the presence of many many further moons within them too.
@Joe Shearer @VCheng @Sinan @Vergennes @xenon5434 @Kartal1 @Saithan @Saiyan0321 @Paro @Gautam @UkroTurk @Webslave @T-123456 @Madokafc @#comcom @Zapper et al.
Heh, well when you go out ice skating and pull your arms in when spinning, you can pirouette helluva fast if you dont watch out.
Hehe, it actually reminded me of a professor I once had when we worked on a satellite design project. One of my louder-brash project-mates kept venturing that we needed to make the reaction wheels bigger and beefier etc...and my prof finally got annoyed with him and just said "uhhh NO, you just make them able to spin FASTER!...SILLY!" ....i.e please recognise what is linear vs squared in the angular momentum rotational stability etc.
Basically getting something to spin incredibly fast relative to its mass, is perfect way to illustrate this like in that clip you posted. With little net gravity field, you can see principal axi easily when you simply impart the high rotational intensity...in effect the reverse of what reaction wheels do.
So true, it is kind of counter intuitive at first glance, but there is sufficient transmission of the harmonics given each metronome concentrated harmonic w.r.t the system connecting them (in this case a plank on some cans, thus allowing fairly unconstrained energy interaction among a low population of items).
This is a more wide ranging phenomenon in the macro scale too...if you look at Resonant interactions at large, with the studies and works of poincare, hamilton, lagrange, fourier etc.
Take orbital resonances for example:
Looking at just Io and Europa for example (Any example will do, incl the planets themselves around the sun):
Shortest distance found between these two bodies (Io and Europa) in their respective orbits is roughly 250,000 km. At this point in time, they exert (due to their masses) about 4.5 *10^18 N on each other using Gmm/r^2.
If we look at Io, we find its centripetal force (mv^2 / R) due to jupiter is about 4.5X10^22 N.
So basically the latter is magnitude of 4 higher (10,000 times higher).
So a 0.01% relative force interaction (applied with enough consistency and time) is enough to achieve massive resonance lock.
(I did the numbers w.r.t distances, velocities and masses really quick without dbl checking so there is potentially an error somewhere , but the concept holds in general given magnitudes here I have explored before, trust me )
Can have a read here coming back to the metronome stuff:
Coincidentally in that paper (given I just brought astronomy into the picture), Huygens (who was first to discover a moon of Saturn i.e Titan) was fascinated by the "ring of saturn", which are now known to be Rings and have a number of interesting resonant phenomenon given the presence of many many further moons within them too.
@Joe Shearer @VCheng @Sinan @Vergennes @xenon5434 @Kartal1 @Saithan @Saiyan0321 @Paro @Gautam @UkroTurk @Webslave @T-123456 @Madokafc @#comcom @Zapper et al.
I went Economy I'm waiting for the "Beautiful Mind" moment... any minute now...Ooooh.....my head aches!
I read HISTORY, for Heavens sake.
I had about Archimedes back in my teenage time while taking diving classes and the exam for my CMAS certificate...It is know that Archimedes has shown a floating -submerged body overflows the liquid as much as its submerged volume,moreover subjected to a lift force related to its submerged volume*density of the liquid.