=?iso-8859-2?Q?IJS_KOLOKVIJ=2C_sreda=2C_28._08._2013; __ob_13._uri; _dr._Mi?= lovan Šuvakov

[Barbara Hrovatin]

Vabimo vas na 21. predavanje iz sklopa "Kolokviji na IJS" v letu 2012/13, ki
bo v sredo, 28. avgusta 2013, ob 13. uri v Veliki predavalnici Instituta
>Jožef Stefan<  na Jamovi cesti 39 v Ljubljani. Napovednik predavanja
najdete tudi na naslovu  <http://www.ijs.si/ijsw/Koledar_prireditev>
http://www.ijs.si/ijsw/Koledar_prireditev, posnetke preteklih predavanj pa
na  <http://videolectures.net/kolokviji_ijs>
http://videolectures.net/kolokviji_ijs. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



dr. Milovan Šuvakov

Institut za fiziko, Beograd, Srbija

 

 

Newtonov problem treh teles: 13 novih periodičnih rešitev in topološka
klasifikacija

 

Problem treh teles sega v l. 1680. Že Isaac Newton je pokazal, da lahko z
zakonom težnosti natančno napove orbito dveh teles, ki ju veze težnost, npr.
zvezde in planeta. Periodična orbita dveh teles je vselej elipsa (v posebnem
primeru krožnica). 

Dve stoletji so znanstveniki na različne načine skušali najti podobno
rešitev za problem treh teles, dokler ni nemški matematik Heinrich Bruns
pokazal, da je iskanje splošne rešitve problema treh teles brezplodno in da
so mogoče le rešitve, ki se nanašajo na posebne primere. Doslej so bile
znane le tri družine breztrkovnih periodičnih orbit: 1) Lagrange-Eulerjeva
(1772), 2) Broucke-Hénonova (1975), in Moorova periodična orbita v obliki
osmice (1993). Tu poročamo o odkritju 13 novih družin periodičnih orbit, s
katerimi število družin naraste na skupaj 16. Predstavimo numerične metode,
s katerimi smo jih odkrili in ločili od drugih, ter naslednje korake v
raziskavah tega problema (npr. določanje stabilnih novih rešitev, ki
ostanejo na tiru tudi, če jih nekoliko perturbiramo). Če je katera od novih
rešitev stabilna, jo morda lahko celo opazimo.

Predavanje bo v angleščini.

Lepo vabljeni!

 

 

*****

 

 

We invite you to the 21st Institute colloquium in the academic year 2012/13.
The colloquium will be held on Wednesday August 28, 2013 at 1 PM in the main
Institute lecture hall, Jamova 39, Ljubljana. To read the abstract click
http://www.ijs.si/ijsw/Koledar_prireditev. Past colloquia are posted on
http://videolectures.net/kolokviji_ijs.

 

********************************************

dr. Milovan Šuvakov

Institute of Physics, Belgrade, Serbia

 

The Newtonian three-body problem: 13 new periodic solutions and topological
classification

 

The three-body problem dates back to the 1680s. Isaac Newton had already
shown that his law of gravity could always predict the orbit of two bodies
held together by gravity, such as a star and a planet, with complete
accuracy. The periodic two-body orbit is always an ellipse (sometimes
turning into a circle). For two centuries, scientists tried different tacks
to find similar solution for three-body problem, until the German
mathematician Heinrich Bruns pointed out that the search for a general
solution for the three-body problem was futile, and that only specific
solutions that work only under particular conditions, were possible. Only
three families of such collisionless periodic orbits were known until
recently: 1) the Lagrange-Euler (1772); 2) the Broucke-Hénon (1975); and 3)
Cris Moore's (1993) periodic orbit of three bodies moving on a "figure-8"
trajectory. We report the discovery of 13 new families of periodic orbits,
bringing the new total to 16. We discuss the numerical methods used to find
them and distinguish them from others, as well as the next steps in this
line of research (e.g. to see how many of the new solutions are stable and
will stay on track if perturbed a little). If some of the solutions are
stable, then they might even be glimpsed in real life.

 

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