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Everything about Orthogonal coordinates
Set of coordinates where the coordinate hypersurfaces all meet at right angles
In mathematics, orthogonal coordinates are defined as a set of d coordinates in which the coordinate hypersurfaces all meet at right angles (note that superscripts are indices, not exponents). A coordinate surface for a particular coordinate qk is the curve, surface, or hypersurface on which qk is a constant. For example, the three-dimensional Cartesian coordinates (x, y, z) is an orthogonal coordinate system, since its coordinate surfaces x = constant, y = constant, and z = constant are planes that meet at right angles to one another, i.e., are perpendicular. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Orthogonal coordinatesA 5-minute orientation
- Skim a recent paper: Structure-dependent electro-elastic analysis of flexoelectric semiconductor curved nanoshells based on the modified couple stress theory in orthogonal curvilinear coordinatesInfluential work since 2022
- Pick up a classic book: Leçons sur les systèmes orthogonaux et les coordonnées curvilignesThe most-reprinted book on the subject
- Read the landmark paper: The calculation of turbulent recirculating flows in general orthogonal coordinatesCited 110 times
- Go sideways: Curvilinear coordinatesA closely related topic
- Go sideways: Skew coordinatesA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The calculation of turbulent recirculating flows in general orthogonal coordinates
Coordinates for molecular dynamics: Orthogonal local systems
Empirical triatomic potential energy surfaces defined over orthogonal bond order coordinates
Strain gradient theory in orthogonal curvilinear coordinates
Transformation optics in orthogonal coordinates
Fast computation of orthogonal Fourier–Mellin moments in polar coordinates
Generation of orthogonal and nearly orthogonal coordinates with gridcontrol near boundaries
The construction of discrete orthogonal coordinates
🆕 Influential since 2022
Structure-dependent electro-elastic analysis of flexoelectric semiconductor curved nanoshells based on the modified couple stress theory in orthogonal curvilinear coordinates
Kinetic Energy Operator of Linear Symmetric Molecules of the A2B2 Type in Polyspherical Orthogonal Coordinates
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces
Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers
Couple Stress-Based Flexoelectric Theory in Orthogonal Curvilinear Coordinates and its Application to an Infinitely Long Dielectric Cylinder
📚 Books worth reading
Leçons sur les systèmes orthogonaux et les coordonnées curvilignesGaston Darboux · 1898- 📕...Lecons sur les systèmes orthogonaux et les coordonnées curvilignesGaston Darboux · 1910
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Curvilinear coordinates In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be…
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- Tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space…
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