Dr. Milovan Šuvakov: The Newtonian three-body problem: 13 new periodic solutions and topological classification

Datum objave: 26. 8. 2013
Kolokvij na IJS
sreda, 28. 8. 2013, ob 13h, Velika predavalnica IJS, Jamova 39, Ljubljana
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, posnetke preteklih predavanj pa na http://videolectures.net/kolokviji_ijs.

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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!

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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.

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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.