the Christoffel symbols

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• Christoffel symbols — In mathematics and physics, the Christoffel symbols, named for Elwin Bruno Christoffel (1829–1900), are numerical arrays of real numbers that describe, in coordinates, the effects of parallel transport in curved surfaces and, more generally,… …   Wikipedia

• Christoffel symbols/Proofs — This article contains proof of formulas in Riemannian geometry which involve the Christoffel symbols. Proof 1 Start with the Bianchi identity: R {abmn;l} + R {ablm;n} + R {abnl;m} = 0,!. Contract both sides of the above equation with a pair of… …   Wikipedia

• Deriving the Schwarzschild solution — The Schwarzschild solution is one of the simplest and most useful solutions of the Einstein field equations (see general relativity). It describes spacetime in the vicinity of a non rotating massive spherically symmetric object. It is worthwhile… …   Wikipedia

• Solving the geodesic equations — is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics. Physically, these represent the paths of (usually ideal) particles with no proper… …   Wikipedia

• Mechanics of planar particle motion — Classical mechanics Newton s Second Law History of classical mechanics  …   Wikipedia

• Centrifugal force (planar motion) — In classical mechanics, centrifugal force (from Latin centrum center and fugere to flee ) is one of the three so called inertial forces or fictitious forces that enter the equations of motion when Newton s laws are formulated in a non inertial… …   Wikipedia

• Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia

• Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   Wikipedia

• Finite strain theory — Continuum mechanics …   Wikipedia

• List of formulas in Riemannian geometry — This is a list of formulas encountered in Riemannian geometry.Christoffel symbols, covariant derivativeIn a smooth coordinate chart, the Christoffel symbols are given by::Gamma {ij}^m=frac12 g^{km} left( frac{partial}{partial x^i} g {kj}… …   Wikipedia

• Connection (mathematics) — In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of… …   Wikipedia