Watch the weird new solutions to the baffling three-body problem
25 May 2018
Watch the weird new solutions to the baffling three-body problem
It takes three to tango
NASA/JPL-CalTech/T. Pyle
By Chelsea Whyte
The infamous three-body problem – the mathematical puzzle of how three objects can orbit one another according to Newton’s laws – now has hundreds of new solutions.
Last year, Shijun Liao at Shanghai Jiaotong University in China and his colleagues used a supercomputer to calculate more than a thousand new solutions, nearly doubling the known number of answers to the three-body problem. Now, they’ve added 231 more ways that three bodies bound together by gravity can orbit one another without colliding.
As before, the new solutions all hinge on periodic
https://www.newscientist.com/article/2170161-watch-the-weird-new-solutions-to-the-baffling-three-body-problem/?cmpid=ILC|NSNS|2018_webpush&utm_medium=ILC&utm_source=NSNS&utm_campaign=webpush-Roost-threebodyprob
(That's all I have, unfortunately, because the rest is behind a paywall. From a quick google trip, this might help.)
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"Chaotic Dynamics" --China Scientists Make New Discoveries for the Three-Body Problem: 'The 3rd Great Revolution in Physics'
October 12, 2017
- click for image -
http://www.dailygalaxy.com/.a/6a00d8341bf7f753ef01bb09cc8742970d-800wi
China's Cixin Liu's The Three-Body Problem (image above) is a stunning science-fiction novel that asks one of the oldest questions in SF: What would it mean for the human race to come in contact with an extraterrestrial intelligence? One of the main characters is a nanotech engineer, who's been swept up in a virtual-reality, online video game called "Three Body" that's so deeply metaphysical, it resembles a cult. When the story reaches its climax, it's unveiled a conspiracy that spans solar systems — one that not only threatens to alter the human race, but the very building blocks of physics that the human species has evolved to understand.
In the end, the biology of the aliens, and the entire reason why they want to contact Earth, relates directly to the three-body problem --can you predict how three objects will orbit each other in a repeating pattern? The problem has baffled scientists for more than 300 years. As a character in the novel notes, “the three-body system is a chaotic system. Tiny perturbations can be endlessly amplified. Its patterns of movement essentially cannot be mathematically predicted.” It is only quite recently that researchers discovered more than three families of solutions to it.
In our real world, The famous three-body problem can be traced back to Isaac Newton in 1680s, thereafter Lagrange, Euler, and Poincare. Studies on the three-body problem leaded to the discovery of the so-called sensitivity dependence of initial condition (SDIC) of chaotic dynamic system.
Chaotic dynamics is widely regarded as the third great scientific revolution in physics in 20th century, comparable to the relativity and the quantum mechanics. Thus, the studies on three-body problem have very important scientific meanings.
More:
http://www.dailygalaxy.com/my_weblog/2017/10/chaotic-dynamics-chinese-scientist-make-new-discoveries-of-the-three-body-problem-the-3rd-great-revo.html
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Periodic orbits for Newtonian planar three-body problem
Xiaoming LI and Shijun LIAO
Shanghai Jiao Tong University, China
Background
The famous three-body problem can be traced back to Newton [1] in 1680s, and attracted many famous mathematicians and physicists such as Euler [2], Lagrange [3] and so on. Poincare [4] found that the first integrals for the motion of three-body system do not exist, and besides orbits of three-body system are rather sensitive to initial conditions. His discovery of the so-called “sensitivity dependence on initial conditions” (SDIC) laid the foundation of modern chaos theory. It well explains why in the 300 years only three families of periodic orbits of three-body system were found by Euler [2] and Lagrange [3], until 1970s when the Broucke-Hadjidemetriou-Henon family of periodic orbits were found [5–9]. The famous figure-eight family was numerically discovered by Moore [10] in 1993 and rediscovered by Chenciner and Montgomery [11] in 2000. In 2013, Suvakov and Dmitrasinovic [12] made a breakthrough to find 13 new distinct periodic orbits by means of numerical methods, which belong to 11 new families. In 2017 Li and Liao [13] found more than six hundred new periodic orbits of three-body system with equal mass, and in 2018 Li et al. [14] further reported more than one thousand new periodic orbits of three-body system with unequal mass. In
2018, Li and Liao [15] reported more than two hundred new collisionless periodic orbits in free-fall three-body problem.
More:
http://numericaltank.sjtu.edu.cn/three-body/three-body.htm
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Thank you!
