A SOLUTION OF THE GODDARD PROBLEM

Abstract

The problem of optimizing the thrust of a vertically ascending rocket is solved here under the assumption of isothermal atmosphere in two important cases: (1) the jet Mach number is sufficiently large; and (2) the drag is a convex function of the velocity. The first case embraces all physical drags and is valid for the Earth; the second extends to all atmospheres, but is restricted to drags that are fairly common. With impulsive boosts in velocity admitted, the solution is shown to contain a finite number of such boosts in the sonic region of the rocket velocity, and to contain no coasting arcs except in the terminal stage. An absolute minimum is proved with the aid of a sufficient condition applicable to problems of optimum control.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1963
Accession Number
AD0409855

Entities

People

  • Boris Garfinkel

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Atmospheres
  • Calculus Of Variations
  • Continuity
  • Equations
  • Euler Equations
  • Inequalities
  • Lagrangian Functions
  • Mach Number
  • Mathematics
  • Military Research
  • New York
  • North Carolina
  • Ordnance Laboratories
  • Space Flight
  • Terminals

Readers

  • Combustion and Flow Dynamics.
  • Operations Research
  • Space Exploration and Orbital Mechanics.