Some Necessary Conditions for Time-Optimal, Fixed-Fuel Transfers Between Coplanar Orbits.

Abstract

Some necessary conditions in terms of the state and costate variables are derived for time-optimal, thrust-coast-thrust (TCT) trajectories between coplanar, cofocal orbits in an inverse-square gravitational field. Assuming impulsive thrusting, the transfer trajectories are determined by solving a quartic polynomial in the square root of the semi-latus rectum of the transfer orbit. The IBM 7094 digital computer was programmed to solve the polynomial and isolate the root leading to the optimal trajectory. Final mass to initial mass ratios are specified, and initial mass is taken as unity. The necessary conditions are derived using plots of constant mass contours in the transfer angle vs. transfer time plane. The conditions are intended to indicate when the TCT trajectory is not optimal and should be replaced by another type of trajectory, such as coast-thrust-coast-thrust (CTCT) or thrust-coast-thrust-coast (TCTC). (Modified author abstract)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1971
Accession Number
AD0770288

Entities

People

  • Ronald C. Tubbs

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Computers
  • Digital Computers
  • Elliptical Orbits
  • Gravitational Fields
  • Orbits
  • Polynomials
  • Square Roots
  • Trajectories
  • Transfer Orbits

Readers

  • Control Systems Engineering.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Space Exploration and Orbital Mechanics.

Technology Areas

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