The Three-Body Problem.

imhotep

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  • Mar 29, 2017
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    No... not the Netflix one.




    PS: Though it's not mentioned in this video both Euler and Lagrange found solutions for special configurations. Five central configurations correspond to the five families of solutions discovered by Euler and Lagrange. Their solutions are the only three-body solutions for which the shape of the triangle does not change as the triangle evolves!
    In the Lagrange solutions, the triangle remains equilateral at each instant. Ever heard of Lagrange Points?

    Later on in the 1900's the Finnish mathematician Karl F Sundman found a generalized solution using an infinite series which converges. But the convergence is very slow and to calculate it took ages.
    But now with AI and fast computing available there are said to be more than 10,000 solutions depending on various initial conditions.

    Note that it most cases one body is always ejected out of the system and the remaining "Binary" system is the stable configuration.
     

    imhotep

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  • Mar 29, 2017
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    Euler provided his solutions in 1767.... Lagrange in 1772. Poincaré went further in 1892 to show that there can be many solutions and the way to go ahead with the generalized approach.
    In 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a Puiseux series.
    Currently more than 10,000 solutions exist but limited to equal mass configurations.
     
    Last edited:

    malakadss

    Well-known member
  • Mar 8, 2009
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    xxx
    No... not the Netflix one.




    PS: Though it's not mentioned in this video both Euler and Lagrange found solutions for special configurations. Five central configurations correspond to the five families of solutions discovered by Euler and Lagrange. Their solutions are the only three-body solutions for which the shape of the triangle does not change as the triangle evolves!
    In the Lagrange solutions, the triangle remains equilateral at each instant. Ever heard of Lagrange Points?

    Later on in the 1900's the Finnish mathematician Karl F Sundman found a generalized solution using an infinite series which converges. But the convergence is very slow and to calculate it took ages.
    But now with AI and fast computing available there are said to be more than 10,000 solutions depending on various initial conditions.

    Note that it most cases one body is always ejected out of the system and the remaining "Binary" system is the stable configuration.

    tfs