معادلة أيكونية

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This page is a translated version of the page Dictionary:Eikonal equation and the translation is 36% complete.
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نوع من معادلات الموجة للموجات التناغمية بحيث تقارن السرعة المحلية V مع سرعة مرجعية V_R (بنفس معنى مقارنة السرعة إلى سرعة الضوء في الفراغ):


Failed to parse (SVG (MathML can be enabled via browser plugin): 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 } ,


حيث n هي مفهرس النفاذ و ∅ هي دالة الموجة. تكون المعادلة صحيحة بشرط أن يكون تغير الخصائص صغيرًا خلال الطول الموجي

والذي يسمى أحيانًا "شرط التردد العالي".

Failed to parse (SVG (MathML can be enabled via browser plugin): 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})} . }

Solutions to the eikonal equation yield a high-frequency or large-wavenumber asymptotic representation of the wave field as a family of rays, represented by ray position and ray direction---the so-called kinematic aspect of wave propagation.

Another form of the eikonal equation is written in terms of the ray direction vector Failed to parse (SVG (MathML can be enabled via browser plugin): 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) } where the gradient of traveltime (or slowness) vector Failed to parse (SVG (MathML can be enabled via browser plugin): 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} } for Failed to parse (SVG (MathML can be enabled via browser plugin): 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 (SVG (MathML can be enabled via browser plugin): 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})} }

thus Failed to parse (SVG (MathML can be enabled via browser plugin): 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) } are the generalized coordinates and Failed to parse (SVG (MathML can be enabled via browser plugin): 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) } are the generalized momenta from Hamiltonian mechanics, and the eikonal equation corresponds to the Hamiltonian function or the Hamilton-Jacobi equation of analytical mechanics.


External links

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Eikonal equation/ar
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