Ecuación Eikonal

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This page is a translated version of the page Dictionary:Eikonal equation and the translation is 100% complete.

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(del griego Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \iota \kappa o \nu } (ikon) que significa "imagen". Una ecuación derivada de la ecuación de onda a través de la sustitución de una solución de prueba de onda harmónica en la ecuación de onda. En una forma de la ecuación eikonal vista en la literatura de la física, la velocidad local Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V } es comparada a la velocidad de referencia Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_R } (análoga a comparar una velocidad a la rapidez de la luz en el vacio):


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \left(\nabla \phi \right)^2 =\left(\frac{V}{V_R}\right)^2=n^2} ,


donde Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle n} es un índice de refracción y la cantidad Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \phi} es identificada como la función de avance de la fase de propagación de onda, la cual es el "tiempo de viaje" de un punto en un frente de onda. El uso del índice de refracción refleja el deseo de los físicos de trabajar con coordenadas sin dimensiones.

Comúnmente en la literatura geofísica, la ecuación eikonal (para ondas escalares) está escrita solo en términos de la velocidad media Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V(\mathbf{x} ) } donde Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mathbf{x} = (x_1,x_2,x_3) } , tal que

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \left(\nabla \phi(\mathbf{x}) \right)^2 = \frac{1}{V^2(\mathbf{x})}. }

Soluciones a la ecuación eikonal producen altas frequencias o largos número de onda, lo cual es una representación asintótica de un campo de onda, como una familia de rayos, representados por la posición y dirección del rayo---también llamado aspecto "cinemático" de la propagación de onda.

Otra forma de la ecuación eikonal está escrita en términos del vector de dirección del rayo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mathbf{p} = (p_1,p_2, p_3) } donde el gradiente del vector del tiempo de viaje (ó "lentitud") Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle p_i = \frac{\partial \phi}{\partial x_i} } para Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle i = 1, 2, 3 }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle p^2 = \mathbf{p} \cdot \mathbf{p} = p_1^2 + p_2^2 + p_3^2 = \frac{1}{V(\mathbf{x})} }

por lo tanto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mathbf{x} = (x_1,x_2,x_3) } son las "coordenadas generalizadas" y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mathbf{p} = (p_1,p_2, p_3) } son el "momento generalizado" de la mecánica Hamiltoniana, y la ecuación eikonal corresponde a la función Hamiltoniana ó la ecuación Hamilton-Jacobi de la mecánica analítica.


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