Forums > Advanced Poi Moves > Third-order Motions (three circles composition)

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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Hi everybody !

I would like to share some stuff about what could be called third order motions.

Currently, we usually know and use second order motion, which are basically relations like Antispins and Inspins : Composition of 2 circles. Notice that this set also includes first order motions, when one of the 2 circles does not spin (a relation i call Nospin).

Consequently, third order motions contains second and first order motions. This lead to a level which enable to describe almost all patterns that we could draw.


Before ... let me explain my vision of what a pattern is (even if it is a paste of one of my previous posts):

To my mind a pattern is a cyclic curve that can be define in a unique way by its frequencies or number of tours ("harmonic" component) and by its radius or lengthes ("modulus" component).

In the field of the 2 circles compositions ... which is for instance the most commonly used ... the "model" is the following :


Non-Https Image Link


O is the shoulder, M is the hand ("Main" in french), E is the Extremity of the object (po, club staff) and Ebis is the other extremity (in the case of the staff).

Theta1 and Theta2 (frequencies or number of turns) define the harmonic part of a pattern whereas Rho1 and Rho2 (radius or length) define the "modulus" part.

Rho=1 when the arm is stretched (when the po is unwrapped).

The patterns will be defined in the following way : Theta1 Theta2 ; Rho1 Rho2.


And now examples :


Non-Https Image Link

Non-Https Image Link


The first example is 1 4 ; 1 1 (if E would have run the other way : -1 -4 ; 1 1)
The second example is 1 -6 ; 1 1 (if E would have run the other way : -1 6 ; 1 1)

As we can see these patterns are in a particular case of "modulus" component ... as the 2 radius or lengthes are equal (in this case ... the simplest ... the values are 1) ... and called "rosettes".

There is another particular "modulus" part mode which give curves called cyclods.

This case happen when the speeds of M and E are equal in the earth (or audience) reference.
It means in terms of maths that Theta2/Theta1=abs(Theta1/(Theta1+Theta2)) (Theta1.abs(Theta1)=Theta2.abs(Theta1+Theta2)).

With the first example (1 4 ; 1 1) above it would give us :


Non-Https Image Link


And it would be called 1 4 ; 1 1/5.

With the example of a 3 foils "rosette" antispin (1 -3 ; 1 1) :


Non-Https Image Link


It would be called 1 -3 ; 1 1/2.


All the cycloids are not feasable ... i mean if we keep the arm stretched (Rho1=1) ... because the differents cases of wraps (thumb excluded) can only take the following values :

Rho2 -> Wrap

1/5 -> 2h+1f
1/4 -> 2h
1/3 -> 1h+3f
2/5 -> 1h+2f
1/2 -> 1h+1f
3/5 -> 4f=1h
2/3 -> 3f
3/4 -> 2f
4/5 -> 1f
1 -> 0f

(h for hand and f for finger)

There is also patterns with more than one arm turn (Theta1>1) ... the most popular example of these kind of pattern would be :

Non-Https Image Link

Non-Https Image Link


AKA 2 -5 ; 1 1 and 2 -5 ; 1 2/3 (if we keep the same sense of running as the examples above)

But there is a lot of other examples like:


Non-Https Image Link

Non-Https Image Link


AKA 3 2 ; 1 1 and 3 2 ; 1 3/5 (rotated by 90 in this image)


Non-Https Image Link
[img:center]http://www.mathcurve.com/courbes2d/epicycloid/epicycloid13.gif[/img]

AKA 3 4 ; 1 1 and 3 4 ; 1 3/7 (rotated by 45 in this image)

In general ... with pos ... antispin patterns have this rule of feasability : abs(Theta1)<abs(Theta2)/2 ... whereas Inspins patterns have this rule of feasability : abs(Theta2)>abs(Theta1)/2.



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DrexFactor
DrexFactor

Defeats the purpose
Location: Washington, DC USA
Member Since: 18th Jul 2007
Total posts: 72
Posted:I'm still catching up on this thread (been in Africa for the past month), but I'd be delighted to host these images. Zalty, can you email them to me? drex (at) drexfactor dot com
EDITED_BY: DrexFactor (1283136576)
EDIT_REASON: hiding my email from spambots


Peace,
Drex

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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Okay guys the images are back ! clap

Great explanations Jon !
Thanks to make me avoid writing a too excessive reply.


Originally Posted By: astonZaltymbunk: I am having trouble deciding what the different trajectories in some of your diagrams are in real terms.

Extremity is logically the poi head, but what would main and centreinter be?

Okay first don't forget that i am french ... so what is written on the pictures is in this language.

"Trajet" means Path, "Centre" means Center, "Main" means Hand & "Extremit" means Extremity in English. "Inter" is for Intermediary as explained before.

So, "Trajet CentreInter" is the path described by the point I, "Trajet Main" is the path described by the point M & "Trajet Extrmit" is the path described by the point E in my model and from the audience poitn of view.

"Relatif" means Relative in English.

So, "Trajet Main Relatif" is the path described by the point M with the point of view of a fly putted on [OI] (as Jon explained before about the local frame reference).
And "Trajet Ext Relatif" is the path described by the point E with that same point of view.


Originally Posted By: UnregistredCan you show your pattern generator sheet ?

I have to do an english version of my excel sheet ... so let me a few days to make it more understainable and i'll send it to Drex in order to make it freely downloadable.


Originally Posted By: AlienJonConcerning the name "no spin". I just want to point out that this makes sense from a particular frame of reference. Specifically if the spin is observed from a frame of reference oriented to the 2nd Center of Rotation, for example a fly sitting on the hand of the poi spinner. If on the other hand, we look from the frame of reference of a stationary audience, then there is spin, but it is "concentric spin", ie concentric to the hand path.

I think Zaltymbank tends to use the local frame of reference, and I tend to use the audience. I'm not saying that one name/concept is better or worse, just want to make sure people know they are the same phenomenon viewed from different frames of reference.

Actually i consider the segments of my model as a linkage which means that the angles and numbers of turns are counted relatively to the previous one. Thus, only [OI] is counted according to the absolute (or audience) reference because it is the first segment.

That type of reference enable to make sense to the numbers as used in the notation as explained before (first post of the topic) because there is a direct correspondance between these ones and the numbers of foils inside the patterns.

It also enables to extract some basic rules of composition (serial & parallel) with simple maths operation (addition and substraction).


A word about Zan's Diamond :

According to the video posted by [ Unregistered ] & Jon, Zan's Diamond and the AAS spinned by Mel in his Video are definitely not the same patterns.

As Jon explained it is based on linear version of hand CAP.
In terms of elementary patterns used for this CAP we have
Non-Https Image Link
and
Non-Https Image Link
AKA 1 -4 ; 3/4 1/4 and 1 -2 ; 1/2 1/2 (they are in cycloid case because it is the closest to the polygonal representation).


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bjrcboy
journeyman

Member Since: 29th Aug 2009
Total posts: 74
Posted:Hand follows a 4p antispin flower while the poi does a 4petal antispin flower




EDITED_BY: bjrcboy (1289278710)


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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:The same pattern (Anti-AntiSpin(4,4) in Open-Open StartMode) in a graphical version :


Non-Https Image Link


If you want to see all the parameters, i have saved this pattern and Mel's pattern seen previously (Anti-AntiSpin(4,2) in Close-Close StartMode) as examples in the Trochod Engine(.xlsx) (or Trochod Engine (.xls))


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MELanholi
MELanholi

multispinner
Location: Russia, Saint - Petersburg
Member Since: 16th Jan 2009
Total posts: 39
Posted:WOW!!! I just find this topic!

Guys, I love you! I am so happy that I am not alone in this searchings!
Nice to see that you and me thinking in the same ways!

I want to know, you guys discover third-order motions same time with me? Or my video was first? (I just shocked, cause this topic looks like a copy of my notebook :D)

sorry for bad English! (


No eat, no drink, no sleep, no f**k! SPIN! SPIN! SPIN!

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aston
aston

Unofficial Chairperson of Squirrel Defense League
Location: South Africa
Member Since: 2nd Dec 2007
Total posts: 4061
Posted:Hi Mel. smile

The first post is from 21/08/2010. I suspect it is one of those ideas that was found by a number of people all at once.


'We're all mad here. I'm mad, you're mad." [said the Cat.]
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "Or you wouldn't have come here."
- Lewis Carroll, Alice's Adventures In Wonderland

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MELanholi
MELanholi

multispinner
Location: Russia, Saint - Petersburg
Member Since: 16th Jan 2009
Total posts: 39
Posted:Well, I think you right!
Anyway I an happy that I am not alone in my searchings (I am not only one theoretical freak :D)!


No eat, no drink, no sleep, no f**k! SPIN! SPIN! SPIN!

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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Hello Mel. Nice to "meet" you !
Aston has right effectively i work on those 3rd order things for a few years now ... and i guess this is something "in the air" that more and more spinners are catching in their mind !
If you have anything to share on these subject please do not hesitate to use this topic as well.
I'll contact you on FB if ever we want to exchange on the notions later !


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meshunderlay
meshunderlay

Juggler/Spinner
Location: Hicksville, New York, USA
Member Since: 15th Sep 2008
Total posts: 612
Posted:Originally Posted By: ZaltymbunkAnd now examples :


Non-Https Image Link

Non-Https Image Link


The first example is 1 4 ; 1 1 (if E would have run the other way : -1 -4 ; 1 1)
The second example is 1 -6 ; 1 1 (if E would have run the other way : -1 6 ; 1 1)



Heya, just a random question about this part specifically, and I'm sorry if this was covered already....

Shouldn't the first example be 1 5 ; 1 1 (4 petal inspin), and the second be 1 -5 ; 1 1 (6 petal antispin)?


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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Hello Mesh smile

Your description is also correct, however you are counting the turns of all the segments (arm & object) in the absolute referential (the earth let's say).

I have chosen to start with an absolute referential : In general it is the half straight line define by the starting position of the arm but let's say it is the one going from the center to the bottom for that case.

Then i count my arm turns relatively to it and i count the object turn relatively to the arm (each time they are aligned for example).

This system is efficient for me in term of notation because it gives meaning to the 2 first numbers.

Example : the description of the pentacle pattern is written 2 -5. 5 fits with the numbers of "petal" and 2 fits with the numbers of jump the object do to go from a petal to another.

I think these kind of keys facilitate a lot the visualization of the pattern once written on a piece of paper into a notation.

Does it make any sense to you ?

EDITED_BY: Zaltymbunk (1322338957)


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meshunderlay
meshunderlay

Juggler/Spinner
Location: Hicksville, New York, USA
Member Since: 15th Sep 2008
Total posts: 612
Posted:Ah, maybe I had misunderstood what the two numbers defined.

I was thinking the first number was number of arm rotations and the second was the number of poi rotations.

For example I was thinking an antispun pentacle would be "2 -3" as the arm makes two full rotations while the poi makes 3.


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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:As i said the numbers does represent the number of rotations (respectively of the arm and of the object) !
The only thing that make a difference in your example is the way these rotations are counted.
If you count it all along the earth or audience referential, you get "2 -3" for the pentacle.
If you count each part of the chain relatively to the previous one (arm/ground ; object/arm), you get "2 -5" which is more meaningfull for visualizing the motion out of the numbers.


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DrexFactor
DrexFactor

Defeats the purpose
Location: Washington, DC USA
Member Since: 18th Jul 2007
Total posts: 72
Posted:Damn, dude...only took me two years to catch up to you on this, Damien wink





Peace,
Drex

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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Nice job for the vid & nice motion execution Drex ! wink
It looks pretty the same than what my sim draw ! eek
Keep practising & Cheers \/

PS : For my own information, what do you call antibrids in the video ?


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DrexFactor
DrexFactor

Defeats the purpose
Location: Washington, DC USA
Member Since: 18th Jul 2007
Total posts: 72
Posted:As it was originally described to me, an antibrid is any hybrid wherein one poi is orbiting around the head of the other poi. I think of it as creating a relationship between one hand and the poi attached to the other hand. If you just refer to them as hybrids, however, you're not wrong wink

Peace,
Drex

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LifeofFire
stranger

Member Since: 2nd Jan 2013
Total posts: 3
Posted:I'm not gonna lie, Reading this WHOLE thing, I can say in 1 week after reading this I have advanced 100x faster. It's opened up all my planes and flowers. Such and amazing thing to read thank you so much!

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Zaltymbunk
Zaltymbunk

newbie
Location: Toulouse, France
Member Since: 6th Jul 2006
Total posts: 38
Posted:Ok Thanks you very much LifeofFire : Delighted to know that those pieces of contents helps !! Cheers smile

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Mtnsailor7
Spinner
Location: Caribean
Member Since: 20th Sep 2012
Total posts: 6
Posted:Woah, really glad I found this! haha

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