Concepts inN-body simulations: The performance of some integrators
N-body simulation
An N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity. In cosmology, they are used to study processes of non-linear structure formation such as the process of forming galaxy filaments and galaxy halos from dark matter in physical cosmology. Direct N-body simulations are used to study the dynamical evolution of star clusters.
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Integrator
An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus. The integration function is often part of engineering and scientific calculations. Mechanical integrators are used in such applications as metering of water flow or electric power. Electronic analog integrators were the basis of analog computers.
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N-body problem
The -body problem is the problem of predicting the motion of a group of celestial objects that interact with each other gravitationally. Solving this problem has been motivated by the need to understand the motion of the Sun, planets and the visible stars. Its first complete mathematical formulation appeared in Isaac Newton's Principia (the -body problem in general relativity is considerably more difficult).
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Symplectic integrator
In mathematics, a symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics and symplectic geometry. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in molecular dynamics, discrete element methods, accelerator physics, and celestial mechanics.
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Truncation
In mathematics and computer science, truncation is the term for limiting the number of digits right of the decimal point, by discarding the least significant ones. For example, consider the real numbers 5.6341432543653654 32.438191288 ¿6.3444444444444 To truncate these numbers to 4 decimal digits, we only consider the 4 digits to the right of the decimal point.
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Round-off error
For the acrobatic movement, roundoff, see Roundoff. 50x40px This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
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Double-precision floating-point format
In computing, double precision is a computer number format that occupies two adjacent storage locations in computer memory. A double-precision number, sometimes simply called a double, may be defined to be an integer, fixed point, or floating point (in which case it is often referred to as FP64). Modern computers with 32-bit storage locations use two memory locations to store a 64-bit double-precision number (a single storage location can hold a single-precision number).
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Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their masses. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, and coalesced matter to remain intact, thus accounting for the existence of the Earth, the Sun, and most of the macroscopic objects in the universe.
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