One stick game...

[iacob alex]

   
    ...can be played, as a pendulum in gravity,from fast to slow swinging motion,in accordance to the placement of the pivot on this one.
       If the pivot is fixed, and we release the pendulum from the top position,in a free up-down fall,without any additional impulse(with no initial velocity),the trajectory of any point of the stick (including the center of weight) is a not completed circle(due to the friction).
       If we add an impulse to the pendulum,in the top position(some initial velocity),we can get a full round trajectory,and a new consecutive fall(s).
          Now,the "game";
       1/the pivot is in your hand
       2/try to move pendulum in a continuous ring-like motion,around the pivot(this time,a mobile fulcrum in your hand).You must use one hand only!!!
       3/have in sight the motion of your hand
       4/try to replace the movements of your hand with a "mechanical as hand" configuration
       5/think about Milkovic's double oscillatory system(pendular lever)
       6/imagine your own system
       7/play it,this game seems to be rewarding

   One of the joys of life,is to keep our curiosity alive.

                  All the Bests!  /  Alex

[iacob alex]

              Hi!

The last message was intended about a pendulum with a mobile fulcrum.
It can be,as a Milkovic's pendulum (  www.veljkomilkovic.com/OscilacijeEng.html  ),or in a more expressive show,as the second and the third pendulum of Alexander Calder's  "Performing Seal" (  www.mcachicago.org/Book/Calder-txt.html  ).

A problem of this kind is more difficult(on paper...),than one of a pendulum with a fixed fulcrum.

If we search on net "Mesodynamics",we can notice some new miraculous facts about the common pendulum(with fixed fulcrum).
Mesodynamics is an unstudied region,whose width is 19 orders  of magnitude,between classical mechanics and quantum mechanics.
Thr first experiment involving mesodynamics(Dr.Peters/Ga/US),is reffered to a long-period pendulum operating at low amplitude.
One of the more fascinating observation of a mass dynamic type is that of the negative damping.
A long period pendulum can be determined by external resources into a "far-from-equilibrium" condition.
Now,when negative damping occurs,the amplitude of the oscillation increases.
In the case of the pendulum,the energy from the oscillation in this negative dumping case,comes from the interaction with the support structures,as a primary supposition,but the research is on the way,so new facts can show up.
A simple -constructed mettalic rod("One stick game..."),played as a pendulum,is capable of demonstrating rich physics in a largely unstudied area.

A rod,a stick is in reality a huge collection,net of atoms,and the atoms do not remain in a fixed lattice position,face to an irrotational gravity field...and side-by -side have an interplay with inertia.
As we can see,the physical pendulum motion is never simple,...it can be a promising domain,for unexpected good news ,that we can use...on our topic.
About "Mesodynamics",take a look at :  http://physics.mercer.edu/petepag/nonlin.htm   
    All the Bests!  /  Alex

[iacob alex]

...can be better understand,if we consider a mass/a stick not as a point mass/center of weight,but as a huge collection,structure,net of atoms.
With that concept,of point mass,applied to electronics...there is no electronics.We must think,in mechanics point masses as connected atoms,as a structure.

Gravity and inertia,the irrotational flow and the isotropic property of space acts on every atomic nucleus.
This action -reaction interplay is so different ,face to the fulcrum/pivot in a pendular motion,if we take into account the relative position of every atom...it's like a long blade in water flow ,when the blade is divided in many,many venetian blindes:some are closed by the flux(collecting power),some are wide opened by the same flow(consuming power).
WM2D obeys the "actual" ,mathematics that is not fitted to describe this situation,of a real large pendular motion.
This kind of consideration can be a possible "key",to understand  oscillators as a gate to the so called chaos,and the same chaos as a real order...a true paradox,nobody knows what we are talking about...if you take a look at   http://news-info.wustl.edu/tips/page/normal/6845.html   
So,the order is inside,or outside?Are we living between two commanding mirrors?

Sure,our problem is more elementary:a stick,as an atomic structure,acts as a pendulum in gravity and inertia.The pendular spectrum is between nonpendulum(the fulcrum is in the middle of the stick,an alltime balaced position),and full pendulum(the fulcrum is at one end of the stick,an easy unbalanced position).Between these extremes ,there is a huge world of possible pendulums to test,study and put into life for some practical  purposes.
   All the Bests!  /  Alex

[iacob alex]

    Hi!

For people interested in the manner that a simple stick is falling in the gravity potential flow,I recommend a very short movie at:       http://myweb.lmv.edu/gvarieschi/chimney/toy2m-forweb.mov 
  Now,you can imagine easy,that a simple stick that plays a swinging motion,can show,as out of the blue,some astonishing features.
  If we imagine,that a simple stick,can be a straight  or any other shape line,we understand that the pendular motion is never...simple.
  Have a fun play...All the Bests!   /  Alex

[iacob alex]

   Hi!
Sorry about a very short mistake:"v" is "u"   so that right address is:    http://myweb.lmu.edu/gvarieschi/chimney/toy2m-forweb.mov

I hope you can find it easy,now.
          All the Bests!  /  Alex