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In numerical analysis, leapfrog integration is a method for numerically integrating differential equations of the form or equivalently of the form particularly in the case of a dynamical system of classical mechanics. Comparison of Euler's and Leapfrog integration energy conserving properties for N bodies orbiting a point source mass.
n. -body problem. In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. [1] Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars.
N. -body simulation. In physics and astronomy, an N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see n -body problem for other applications). N -body simulations are widely used tools in astrophysics, from investigating the dynamics of few-body systems like ...
Prony analysis of a time-domain signal. Prony analysis ( Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer. [1] Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampled signal and builds a series of damped complex ...
In quantum mechanics, notably in quantum information theory, fidelity quantifies the "closeness" between two density matrices. It expresses the probability that one state will pass a test to identify as the other. It is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space.
n ! {\displaystyle n!} In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.
SciPy. SciPy (pronounced / ˈsaɪpaɪ / "sigh pie" [2]) is a free and open-source Python library used for scientific computing and technical computing. [3] SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and ...
Python is a free, text-based programming language that has already been used by those who do physics research to great effect. But students can also learn to use it and, through its use, learn other aspects of physics--especially ones that are difficult or impossible to perform as physical labs.