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Application of the optimization method to the point-to-point radio …
https://ieeexplore.ieee.org/document/8113427#:~:text=In%20direct%20variational%20methods%2C%20some%20trajectory%20is%20transformed,not%20widely%20known%20in%20ionospheric%20point-to-point%20ray%20tracing.
Variational methods in ionospheric ray tracing | Request …
https://www.researchgate.net/publication/252053386_Variational_methods_in_ionospheric_ray_tracing
Request PDF | Variational methods in ionospheric ray tracing | form only given: Ray tracing is an important tool in the study of radio wave propagation. In particular, numerical solutions to the ...
Point‐to‐point ionospheric ray tracing by a direct …
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2011RS004748
Point-to-point ionospheric ray tracing by a direct …
https://ieeexplore.ieee.org/abstract/document/7776244/
Point-to-point ionospheric ray tracing by a direct variational method. Abstract:While the Haselgrove ray tracing equations are well suited to situations where the ray launch direction is known, they are less effective for situations where only the end points of the ray are known. In such cases, many rays must be traced from the launch point in order to home in on the landing …
Variational methods in ionospheric ray tracing - INFONA
https://www.infona.pl/resource/bwmeta1.element.ieee-art-000006050876
This principle provides a variational equation for ray tracing and such equations are better suited to the solution of point to point ray tracing problems. The present paper will discuss the problems of directly solving Fermats principle and describe some recent work that has led to a successful variational approach to ionospheric ray tracing with magneto-ionic effects included.
Point-to-point ionospheric ray tracing by a direct …
https://www.researchgate.net/publication/251428927_Point-to-point_ionospheric_ray_tracing_by_a_direct_variational_method
Direct variational method for the point-to-point ionospheric ray tracing was proposed by Smilauer (1970) who derived ordinary differential equations for the radio ray and solved them using a ...
Point-to-point ionospheric ray tracing by a direct variational …
https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011RS004748
point ray tracing. [3] Section 2 of this paper discusses Fermat’s principle, the basic variational principle of ray tracing. It is shown that a partial solution of the Haselgrove equations can be used to reduce this variational principle to a form that is more con-venient for studying ray tracing. Section 3 discusses the
Comparison оf Shooting Method and Variational …
https://link.springer.com/article/10.3103/S1062873821030114
The most important contribution to developing and using direct approach for point-to-point ray tracing was made by C.J. Coleman , who proposed a comprehensive variational method that allows us to use simple minimization in searching for the high (Pedersen) and transionospheric rays. Low rays were found by numerically solving the variational equation.
Progress in radio ray tracing in the ionosphere | URSI …
https://ieeexplore.ieee.org/abstract/document/7909439/
Methods of efficiently calculating field strength, Doppler shift, and absorption of the waves are discussed, based on a variational formulation. Some history of the evolution of ionospheric radio ray tracing is given. Numerical and analytic or closed-form ray tracing are contrasted, and guidance is given on the choice of appropriate technique ...
Ionospheric Ray Tracing
https://farside.ph.utexas.edu/teaching/jk1/lectures/node95.html
Ionospheric Ray Tracing. Suppose that we possess a radio antenna that is capable of launching radio waves of constant frequency into the ionosphere at an angle to the vertical. Let us consider the paths traced out by these waves in the - plane. For the sake of simplicity, we shall assume that the waves are horizontally polarized, so that the electric field vector always lies parallel to the …
Point-to-point ionospheric ray tracing by a direct …
https://ui.adsabs.harvard.edu/abs/2011RaSc...46.5016C/abstract
While the Haselgrove ray tracing equations are well suited to situations where the ray launch direction is known, they are less effective for situations where only the end points of the ray are known. In such cases, many rays must be traced from the launch point in order to home in on the landing point. An alternative approach is to directly solve the variational principle from which …
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