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  2. Exact solutions of classical central-force problems - Wikipedia

    en.wikipedia.org/wiki/Exact_solutions_of...

    A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, with an Introduction to the Problem of Three Bodies (4th ed.). New York: Dover Publications. ISBN 978-0-521-35883-5. Izzo,D. and Biscani, F. (2014). Exact Solution to the constant radial acceleration problem.

  3. Exact solutions in general relativity - Wikipedia

    en.wikipedia.org/wiki/Exact_solutions_in_general...

    These tensor fields should obey any relevant physical laws (for example, any electromagnetic field must satisfy Maxwell's equations).Following a standard recipe which is widely used in mathematical physics, these tensor fields should also give rise to specific contributions to the stress–energy tensor. [1]

  4. Three-body problem - Wikipedia

    en.wikipedia.org/wiki/Three-body_problem

    An animation of the figure-8 solution to the three-body problem over a single period T ≃ 6.3259 [13] 20 examples of periodic solutions to the three-body problem. In the 1970s, Michel Hénon and Roger A. Broucke each found a set of solutions that form part of the same family of solutions: the Broucke–Hénon–Hadjidemetriou family. In this ...

  5. Euler's three-body problem - Wikipedia

    en.wikipedia.org/wiki/Euler's_three-body_problem

    The Euler three-body problem is known by a variety of names, such as the problem of two fixed centers, the Euler–Jacobi problem, and the two-center Kepler problem. The exact solution, in the full three dimensional case, can be expressed in terms of Weierstrass's elliptic functions [2] For convenience, the problem may also be solved by ...

  6. Newton's laws of motion - Wikipedia

    en.wikipedia.org/wiki/Newton's_laws_of_motion

    If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in closed form. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions ...

  7. Solutions of the Einstein field equations - Wikipedia

    en.wikipedia.org/wiki/Solutions_of_the_Einstein...

    But if one requires an exact solution or a solution describing strong fields, the evolution of both the metric and the stress–energy tensor must be solved for at once. To obtain solutions, the relevant equations are the above quoted EFE (in either form) plus the continuity equation (to determine the evolution of the stress–energy tensor):

  8. Two-body problem in general relativity - Wikipedia

    en.wikipedia.org/wiki/Two-body_problem_in...

    More recently, it has become possible to solve Einstein's field equation using a computer [1] [2] [3] instead of mathematical formulae. As the two bodies orbit each other, they will emit gravitational radiation ; this causes them to lose energy and angular momentum gradually, as illustrated by the binary pulsar PSR B1913+16 .

  9. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/Navier–Stokes_existence...

    In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...

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