Live briefing
Everything about Paraboloidal coordinates
Three-dimensional orthogonal coordinate system
Paraboloidal coordinates are three-dimensional orthogonal coordinates that generalize two-dimensional parabolic coordinates. They possess elliptic paraboloids as one-coordinate surfaces. As such, they should be distinguished from parabolic cylindrical coordinates and parabolic rotational coordinates, both of which are also generalizations of two-dimensional parabolic coordinates. The coordinate surfaces of the former are parabolic cylinders, and the coordinate surfaces of the latter are circular paraboloids. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Paraboloidal coordinatesA 5-minute orientation
- Pick up a classic book: Über parabolische coordinaten und die geodätischen linien auf dem elliptischen paraboloid ..The most-reprinted book on the subject
- Read the landmark paper: XC.Paraboloidal coordinatesCited 3 times
- Go sideways: Maxwell's equations in curved spacetimeA closely related topic
- Go sideways: Relativistic Lagrangian mechanicsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
XC.Paraboloidal coordinates
Laplace boundary-value problem in paraboloidal coordinates
The momentum representation of the hydrogen atom in paraboloidal coordinates
An Approach to Maxwell Equations in Circular Paraboloidal Coordinates by Newman-Penrose Method
Velocity and acceleration in paraboloidal coordinates
📚 Books worth reading
- 📕Über parabolische coordinaten und die geodätischen linien auf dem elliptischen paraboloid ..Ferdinand Groscurth · 1887
Über parabolische Coordinaten u. die geodätischen Linien auf dem elliptischen ParaboloidFerdinand Groscurth · 1887
Analytical solid geometry · 2007
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Maxwell's equations in curved spacetime In physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may deviate…
- Relativistic Lagrangian mechanics In theoretical physics, relativistic Lagrangian mechanics is Lagrangian mechanics applied in the context of special relativity and general relativity.…
- Ellipsoidal coordinates Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system ( λ , μ , ν ) {\displaystyle (\lambda ,\mu ,\nu )} that generalizes the two-dimensi…
- Geodesics in general relativity In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from…
- Dirac equation in curved spacetime In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime (Minkowski space) to curved…
- Polyakov action In physics, the Polyakov action is an action of the two-dimensional conformal field theory describing the worldsheet of a string in string theory. It was…
- Belinfante–Rosenfeld stress–energy tensor In mathematical physics, the Belinfante–Rosenfeld tensor is a modification of the stress–energy tensor that is constructed from the canonical stress–energy…
- Affine gauge theory In mathematical physics, an affine gauge theory is a classical gauge theory in which the gauge fields are affine connections on the tangent bundle over…