An Efficient Algorithm for Computing the Q-Guidance Matrix

Abstract

This paper derives a new method for computing the Q-guidance matrix. This matrix is defined as the derivative with respect to position of the correlated velocity V sub C; i.e., the velocity required to reach a given target in a specified time in an inverse-square gravitational field. The method is completely analytic and yields a simple and efficient algorithm. The analytic equation for the partial derivative of the horizontal component of correlated velocity with respect to range angle developed here is also of independent interest. To the author's knowledge, no such expression for this quantity in terms of the given conditions and the components of V sub C has been derived previously. This equation, in conjunction with the others given here, makes it possible to compute virtually any (first order) derivative of V sub C of interest. The Q-matrix algorithm is of use primarily in the analysis and modeling of guidance systems using some form of V sub G steering.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA064816

Entities

People

  • William L. Davis

Organizations

  • Naval Surface Warfare Center Dahlgren Division

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Angular Momentum
  • Ballistic Missiles
  • Classification
  • Coefficients
  • Computations
  • Coordinate Systems
  • Equations
  • Gravitational Fields
  • Gravity
  • Guidance
  • Iterations
  • Plastic Explosives
  • Security
  • Steering
  • Three Dimensional
  • Trajectories

Readers

  • Approximation Theory.
  • Control Systems Engineering.