STUDIES IN RADAR CROSS SECTIONS. XLIV. INTEGRAL REPRESENTATIONS OF SOLUTIONS OF THE HELMHOLTZ EQUATION WITH APPLICATION TO DIFFRACTION BY A STRIP

Abstract

A class of solutions is derived of the two dimensional Helmholtz equation which satisfied particularly simple boundary conditions. These were used to construct a double integral equation for the Green's function for a line segment. When the line segment was infinite a double integral representation was obtained of the difference of two Hankel functions (line sources). For the case when the line was semi-infinite the known result for the Green's function was used to obtain, via the integral equation, an integral representation for this same Green's function. This integral form, when properly interpreted, led to the corresponding form for the Green's function for a finite segment and this assertion was verified. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1961
Accession Number
AD0253052

Entities

People

  • R. Timman
  • R.e. Kleinman

Organizations

  • University of Michigan

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Diffraction
  • Equations
  • Helmholtz Equations
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Radar Cross Sections
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering