A Second Order Method for Computing an Optimal Re-Entry Trajectory Using Numerical Derivatives.

Abstract

The primary purpose of the study was to investigate a second order method using numerical derivatives to converge to an optimal set of initial costates that would produce an optimal re-entry trajectory. A second objective of the research was to test the computational method by computing a minimum total heat input trajectory (two dimensional) for a lifting body. It was assumed that the vehicle could attain a maximum lift-to-drag of 2.0 during its desent from a near earth orbit. The initial states are known, the initial costates are unknown, and only the final altitude at a fixed final range is specified. The second order method uses the first and second difference equations to iterate on corrections to an arbitrarily chosen set of initial costates. The corrections are based on minimizing a scalar terminal error function. The results indicate that the numerical integration errors limit too severely the accuracy to which the second partials of the terminal errors with respect to the initial costates could be estimated. (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1973
Accession Number
AD0768381

Entities

People

  • David Richards

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Earth Orbits
  • Equations
  • Errors
  • Lifting Bodies
  • Mathematical Analysis
  • Numerical Integration
  • Orbits
  • Terminals
  • Trajectories
  • Two Dimensional

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space
  • Space - Orbital Debris
  • Space - Spacecraft Maneuvers