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The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
A periodic motion is a closed curve in phase space. That is, for some period, ′ = (,), = (). The textbook example of a periodic motion is the undamped pendulum.. If the phase space is periodic in one or more coordinates, say () = (+), with a vector [clarification needed], then there is a second kind of periodic motions defined by
In the classical central-force problem of classical mechanics, some potential energy functions () produce motions or orbits that can be expressed in terms of well-known functions, such as the trigonometric functions and elliptic functions. This article describes these functions and the corresponding solutions for the orbits.
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by ...
In perturbation theory, the Poincaré–Lindstedt method or Lindstedt–Poincaré method is a technique for uniformly approximating periodic solutions to ordinary differential equations, when regular perturbation approaches fail.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
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