Asymptotic Analysis of the Roots of a Certain Transcendental Equation.

Abstract

The spatial eigenvalues that occurred first in the Stewartson-Wedemeyer theory and then in later theories consist of a denumerable basic set which are 0(1) for RE infinity. In this report the existence of an additional single, isolated eigenvalue that is 0(Re raised to the 1/2 power) is demonstrated. The former were used in several reports on liquid-filled projectiles; the latter was undetected in previous work. Asymptotic analysis for RE infinity is used to give accurate estimates for the new eigenvalue. Numerically it is shown that for 10 < RE < 1000 and 0.1 < or = tau 1.0 the formulus from asymptotic analysis must be used rather than those in the original CDC program. The limiting case of nutational frequency approaching spin frequency is also discussed. The effect of the new eigenvalue on previous results, for Re > 1000, is negligible but for Re < 1000 the effect is significant. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1986
Accession Number
ADA168315

Entities

People

  • Nathan Gerber
  • Raymond Sedney

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aeronautics
  • Angular Motion
  • Asymptotic Series
  • Computational Science
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Equations
  • Jet Propulsion
  • Liquid Filled Projectiles
  • Mathematics
  • Mechanics
  • Military Research
  • Physics
  • Physics Laboratories
  • Projectiles
  • Solid Bodies

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • ballistics.