Accession Number:

AD0870495

Title:

The Numerical Evaluation of a Certain Integral with a Rapidly Oscillating Integrand.

Descriptive Note:

Technical memo.,

Corporate Author:

SACLANT ASW RESEARCH CENTRE LA SPEZIA (ITALY)

Personal Author(s):

Report Date:

1970-03-15

Pagination or Media Count:

24.0

Abstract:

This Memorandum considers the numerical evaluation of integrals of the form over the range from 0 to t, the integral eto the alpha times S power, times sin 2Wsub 0S, times the -32 power of the quantity d squared the square of Ysub 0-VS, times ds by two methods. The first is conventional. The second is unconventional and exploits the possibility of expanding the expression dsquared Ysub 0-VSSquared in terms of Legendre polynomials. The integrals whose evaluation is discussed, arose in the study of the following problem. A sinusoidal source, with strength that falls off as the inverse cube of the distance from the source, moves in a straight line past a receiver with velocity much smaller than the field propagation velocity.

Subject Categories:

  • Theoretical Mathematics
  • Cybernetics
  • Radiofrequency Wave Propagation

Distribution Statement:

APPROVED FOR PUBLIC RELEASE