ON THE USE OF THE CALCULUS OF VARIATIONS IN TRAJECTORY OPTIMIZATION PROBLEMS,

Abstract

The theory of the calculus of variations is reviewed, including such subjects as the EulerLagrange equations, the transversality condition, the problems of Bolza, Lagrange, and Mayer, the corner condition, and the Weierstrass condition. Applications to a number of problems are given. These include that of a damped harmonic oscillator that is to be brought to rest in the shortest possible time. This problem is sufficiently simple to allow a clear demonstration of the theory. The close relationship between the ballistic perturbation theory and the calculus of variations is explained. The perturbation theory is then applied to the case of the trajectory in a constant gravity field. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1963
Accession Number
AD0420116

Entities

People

  • D. G. Stechert

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Calculus
  • Calculus Of Variations
  • Demonstrations
  • Equations
  • Mathematics
  • Optimization
  • Perturbation Theory
  • Perturbations
  • Trajectories

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Operations Research