elliptic cylindrical coordinates - meaning, definition, translation, pronunciation
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elliptic cylindrical coordinates (english) - meaning, definition, translation, pronunciation


Part of Speech

Phonetic Transcription

/ɪˈlɪptɪk ˈsɪlɪndrɪkəl kɔːrˈdɪnət͡s/

Meaning

Elliptic cylindrical coordinates are a three-dimensional coordinate system that extends the concept of cylindrical coordinates. In this system, the position of a point in space is defined by three coordinates: the distance from a focal point (similar to radial distance in polar coordinates), the angle in the plane relative to one of the axes, and the height or 'z-coordinate' above the base plane. This coordinate system can be particularly useful in solving partial differential equations and in mathematical physics.

Usage

Elliptic cylindrical coordinates are primarily used in advanced mathematics, physics, and engineering contexts, especially within fields dealing with partial differential equations, wave equations, and certain geometrical considerations. Usage of this term is more prevalent in written forms, such as academic papers and textbooks, rather than in spoken language.

Examples

  1. Elliptic cylindrical coordinates provide a convenient framework for solving Laplace's equation in elliptical geometries.
  2. Translation: Elliptic cylindrical coordinates ofrecen un marco conveniente para resolver la ecuación de Laplace en geometrías elípticas.

  3. Many problems in electromagnetic theory can be simplified using elliptic cylindrical coordinates.

  4. Translation: Muchos problemas en la teoría electromagnética pueden simplificarse utilizando coordenadas cilíndricas elípticas.

  5. The transformation from Cartesian to elliptic cylindrical coordinates is achieved through specific mathematical relationships.

  6. Translation: La transformación de coordenadas cartesianas a coordenadas cilíndricas elípticas se logra a través de relaciones matemáticas específicas.

Idiomatic Expressions

While "elliptic cylindrical coordinates" is mainly a technical term and not commonly featured in idiomatic expressions, mathematical terminology often gives rise to specialized phrases. Here are a few related expressions:

  1. In the coordinates of the ellipse
  2. Working in the coordinates of the ellipse can streamline many engineering calculations.
  3. Translation: Trabajar en las coordenadas de la elipse puede agilizar muchos cálculos de ingeniería.

  4. Mapping to cylindrical forms

  5. The process of mapping to cylindrical forms can often make the math easier to visualize.
  6. Translation: El proceso de mapear a formas cilíndricas a menudo puede facilitar la visualización de las matemáticas.

  7. Transforming into elliptical dimensions

  8. Transforming into elliptical dimensions is crucial when dealing with certain types of wave patterns.
  9. Translation: Transformarse en dimensiones elípticas es crucial al tratar con ciertos tipos de patrones de onda.

Etymology

The term elliptic originates from the Latin word "ellipticus," which means "pertaining to an ellipse," while the term cylindrical derives from the Greek word "ky lindros," meaning "of a cylinder." The combination reflects the geometrical properties involved in this coordinate system.

Synonyms and Antonyms

Synonyms

Antonyms



25-07-2024