Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Curvilinear_coordinates> ?p ?o }
- Curvilinear_coordinates abstract "In geometry, 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 coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R3) are Cartesian, cylindrical and spherical polar coordinates. A Cartesian coordinate surface in this space is a plane; for example z = 0 defines the x-y plane. In the same space, the coordinate surface r = 1 in spherical polar coordinates is the surface of a unit sphere, which is curved. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate systems.Curvilinear coordinates are often used to define the location or distribution of physical quantities which may be, for example, scalars, vectors, or tensors. Mathematical expressions involving these quantities in vector calculus and tensor analysis (such as the gradient, divergence, curl, and Laplacian) can be transformed from one coordinate system to another, according to transformation rules for scalars, vectors, and tensors. Such expressions then become valid for any curvilinear coordinate system.Depending on the application, a curvilinear coordinate system may be simpler to use than the Cartesian coordinate system. For instance, a physical problem with spherical symmetry defined in R3 (for example, motion of particles under the influence of central forces) is usually easier to solve in spherical polar coordinates than in Cartesian coordinates. Equations with boundary conditions that follow coordinate surfaces for a particular curvilinear coordinate system may be easier to solve in that system. One would for instance describe the motion of a particle in a rectangular box in Cartesian coordinates, whereas one would prefer spherical coordinates for a particle in a sphere. Spherical coordinates are one of the most used curvilinear coordinate systems in such fields as Earth sciences, cartography, and physics (in particular quantum mechanics, relativity), and engineering.".
- Curvilinear_coordinates thumbnail Curvilinear.svg?width=300.
- Curvilinear_coordinates wikiPageExternalLink CurvilinearCoordinates.html.
- Curvilinear_coordinates wikiPageExternalLink derivationofunitvectorsincurvilinearcoordinates.
- Curvilinear_coordinates wikiPageExternalLink curvilinear.pdf.
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- Curvilinear_coordinates wikiPageRevisionID "675828256".
- Curvilinear_coordinates wikiPageWikiLink Affine_coordinate_system.
- Curvilinear_coordinates wikiPageWikiLink Albert_Einstein.
- Curvilinear_coordinates wikiPageWikiLink Atlas_(topology).
- Curvilinear_coordinates wikiPageWikiLink Basis_(linear_algebra).
- Curvilinear_coordinates wikiPageWikiLink Bijection.
- Curvilinear_coordinates wikiPageWikiLink Boundary_conditions.
- Curvilinear_coordinates wikiPageWikiLink Boundary_value_problem.
- Curvilinear_coordinates wikiPageWikiLink Cartesian_coordinate.
- Curvilinear_coordinates wikiPageWikiLink Cartesian_coordinate_system.
- Curvilinear_coordinates wikiPageWikiLink Cartesian_product.
- Curvilinear_coordinates wikiPageWikiLink Cartography.
- Curvilinear_coordinates wikiPageWikiLink Category:Coordinate_systems.
- Curvilinear_coordinates wikiPageWikiLink Category:Metric_tensors.
- Curvilinear_coordinates wikiPageWikiLink Central_force.
- Curvilinear_coordinates wikiPageWikiLink Centrifugal_force.
- Curvilinear_coordinates wikiPageWikiLink Chain_rule.
- Curvilinear_coordinates wikiPageWikiLink Christoffel_symbols.
- Curvilinear_coordinates wikiPageWikiLink Circular_symmetry.
- Curvilinear_coordinates wikiPageWikiLink Coefficient_matrix.
- Curvilinear_coordinates wikiPageWikiLink Continuum_mechanics.
- Curvilinear_coordinates wikiPageWikiLink Coordinate_line.
- Curvilinear_coordinates wikiPageWikiLink Coordinate_system.
- Curvilinear_coordinates wikiPageWikiLink Coordinate_vector.
- Curvilinear_coordinates wikiPageWikiLink Coordinates.
- Curvilinear_coordinates wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Curvilinear_coordinates wikiPageWikiLink Covariant_derivative.
- Curvilinear_coordinates wikiPageWikiLink Cross_product.
- Curvilinear_coordinates wikiPageWikiLink Curl_(mathematics).
- Curvilinear_coordinates wikiPageWikiLink Curvilinear_coordinates.
- Curvilinear_coordinates wikiPageWikiLink Curvilinear_perspective.
- Curvilinear_coordinates wikiPageWikiLink Cylindrical_coordinate_system.
- Curvilinear_coordinates wikiPageWikiLink Del.
- Curvilinear_coordinates wikiPageWikiLink Del_in_cylindrical_and_spherical_coordinates.
- Curvilinear_coordinates wikiPageWikiLink Diffeomorphism.
- Curvilinear_coordinates wikiPageWikiLink Differentiable_manifold.
- Curvilinear_coordinates wikiPageWikiLink Differential_of_a_function.
- Curvilinear_coordinates wikiPageWikiLink Differential_topology.
- Curvilinear_coordinates wikiPageWikiLink Divergence.
- Curvilinear_coordinates wikiPageWikiLink Domain_of_a_function.
- Curvilinear_coordinates wikiPageWikiLink Dot_product.
- Curvilinear_coordinates wikiPageWikiLink Earth_science.
- Curvilinear_coordinates wikiPageWikiLink Earth_sciences.
- Curvilinear_coordinates wikiPageWikiLink Engineering.
- Curvilinear_coordinates wikiPageWikiLink Euclidean_space.
- Curvilinear_coordinates wikiPageWikiLink Euclidean_vector.
- Curvilinear_coordinates wikiPageWikiLink Fluid_mechanics.
- Curvilinear_coordinates wikiPageWikiLink Frenet–Serret_formulas.
- Curvilinear_coordinates wikiPageWikiLink Gabriel_Lamé.
- Curvilinear_coordinates wikiPageWikiLink General_relativity.
- Curvilinear_coordinates wikiPageWikiLink Geometry.
- Curvilinear_coordinates wikiPageWikiLink Gradient.
- Curvilinear_coordinates wikiPageWikiLink Integral.
- Curvilinear_coordinates wikiPageWikiLink Integration_(mathematics).
- Curvilinear_coordinates wikiPageWikiLink Introduction_to_the_mathematics_of_general_relativity.
- Curvilinear_coordinates wikiPageWikiLink Invariant_(mathematics).
- Curvilinear_coordinates wikiPageWikiLink Inverse_element.
- Curvilinear_coordinates wikiPageWikiLink Inverse_function_theorem.
- Curvilinear_coordinates wikiPageWikiLink Invertible.
- Curvilinear_coordinates wikiPageWikiLink Jacobian_matrix.
- Curvilinear_coordinates wikiPageWikiLink Jacobian_matrix_and_determinant.
- Curvilinear_coordinates wikiPageWikiLink Laplace_operator.
- Curvilinear_coordinates wikiPageWikiLink Laplacian.
- Curvilinear_coordinates wikiPageWikiLink Levi-Civita_symbol.
- Curvilinear_coordinates wikiPageWikiLink Line_integral.
- Curvilinear_coordinates wikiPageWikiLink Linear_algebra.
- Curvilinear_coordinates wikiPageWikiLink Linear_combination.
- Curvilinear_coordinates wikiPageWikiLink Linear_map.
- Curvilinear_coordinates wikiPageWikiLink Linear_operator.
- Curvilinear_coordinates wikiPageWikiLink Manifold.
- Curvilinear_coordinates wikiPageWikiLink Maxwells_equations.
- Curvilinear_coordinates wikiPageWikiLink Mechanics.
- Curvilinear_coordinates wikiPageWikiLink Metamaterial.
- Curvilinear_coordinates wikiPageWikiLink Metamaterials.
- Curvilinear_coordinates wikiPageWikiLink Metric_(mathematics).
- Curvilinear_coordinates wikiPageWikiLink Metric_tensor.
- Curvilinear_coordinates wikiPageWikiLink Origin_(mathematics).
- Curvilinear_coordinates wikiPageWikiLink Orthogonal.
- Curvilinear_coordinates wikiPageWikiLink Orthogonal_coordinates.
- Curvilinear_coordinates wikiPageWikiLink Orthogonal_vector.
- Curvilinear_coordinates wikiPageWikiLink Orthogonality.
- Curvilinear_coordinates wikiPageWikiLink Partial_derivative.
- Curvilinear_coordinates wikiPageWikiLink Permutation_symbol.
- Curvilinear_coordinates wikiPageWikiLink Perpendicular.
- Curvilinear_coordinates wikiPageWikiLink Physics.
- Curvilinear_coordinates wikiPageWikiLink Plate_theory.
- Curvilinear_coordinates wikiPageWikiLink Position_(vector).
- Curvilinear_coordinates wikiPageWikiLink Position_vector.
- Curvilinear_coordinates wikiPageWikiLink Quantum_mechanics.
- Curvilinear_coordinates wikiPageWikiLink Raising_and_lowering_indices.
- Curvilinear_coordinates wikiPageWikiLink Real_number.
- Curvilinear_coordinates wikiPageWikiLink Real_numbers.