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Spherical Coordinates

Concept

Del in cylindrical and spherical coordinates

This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by : it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by : it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.

Concept

Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.

Concept

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 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.

Concept

Orthogonal coordinates

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.

Concept

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

Concept

Vector fields in cylindrical and spherical coordinates

Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken in comparing different sources. Vectors are defined in cylindrical coordinates by (ρ, φ, z), where ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.

Course

PHYS-101(a): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

Course

PHYS-101(en): General physics : mechanics (English)

Students will learn the principles of mechanics to enable a better understanding of physical phenomena, such as the kinematics and dyamics of point masses and solid bodies. Students will acquire the c

Course

PHYS-101(f): General physics : mechanics

Course

PHYS-101(c): General physics : mechanics (IN)

Lecture

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Lecture

Surface Orientation: Parameterization and Edge Configuration

Covers the parameterization of surfaces and the orientation of surface edges, emphasizing the importance of selecting the appropriate orientation and configuration.

Lecture

Coordinate Systems: Spherical Coordinates

Explores spherical coordinates, trajectory equations, and circular motion in different reference frames.

Lecture

Spherical Coordinates: Determinant of Jacobi

Covers spherical coordinates and the determinant of Jacobi in linear algebra.

Lecture

Rotations: Fixed Points and Spherical Coordinates

Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.

Lecture

Coordinate Systems: Spherical Coordinates

Covers unit vectors, rotations, and accelerations in spherical coordinates for physics applications.

Lecture

Physics 1: Harmonic Oscillator and Spherical Coordinates

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Lecture

Advanced Analysis II: Spherical Coordinates

Covers spherical coordinates, transformations, and volume calculations in integrals.

Publication

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Search Results

Spherical Coordinates

Concept

Del in cylindrical and spherical coordinates

Concept

Cylindrical coordinate system

Concept

Curvilinear coordinates

Concept

Orthogonal coordinates

Concept

Three-dimensional space

Concept

Vector fields in cylindrical and spherical coordinates

Course

PHYS-101(a): General physics : mechanics

Course

PHYS-101(en): General physics : mechanics (English)

Course

PHYS-101(f): General physics : mechanics

Course

PHYS-101(c): General physics : mechanics (IN)

Lecture

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Lecture

Surface Orientation: Parameterization and Edge Configuration

Covers the parameterization of surfaces and the orientation of surface edges, emphasizing the importance of selecting the appropriate orientation and configuration.

Lecture

Coordinate Systems: Spherical Coordinates

Explores spherical coordinates, trajectory equations, and circular motion in different reference frames.

Lecture

Spherical Coordinates: Determinant of Jacobi

Covers spherical coordinates and the determinant of Jacobi in linear algebra.

Lecture

Rotations: Fixed Points and Spherical Coordinates

Covers rotations around fixed points and spherical coordinates, discussing cinematic moments and angular velocity.

Lecture

Coordinate Systems: Spherical Coordinates

Covers unit vectors, rotations, and accelerations in spherical coordinates for physics applications.

Lecture

Physics 1: Harmonic Oscillator and Spherical Coordinates

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Lecture

Advanced Analysis II: Spherical Coordinates

Covers spherical coordinates, transformations, and volume calculations in integrals.

Publication

Spherical Coordinates

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Spherical Coordinates

Local invertibility and sensitivity of atomic structure-feature mappings

High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics