The Two-Point Boundary Version of the Problem of Two Bodies

Abstract

Hamilton-Jacobi's equation for the problem of two bodies in bipolar coordinates is solved in closed form; Stumpff's transcendental functions are used to express a complete solution of it in a universal form. This characteristic function is shown to be the source of the analytical expressions necessary to solve the two-point boundary version of the problem of two bodies. In particular, it establishes immediately Lambert's equation in its universal form.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1970
Accession Number
AD0708170

Entities

People

  • Andre Deprit

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebraic Functions
  • Angular Momentum
  • Boundaries
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Equations
  • Hamiltonian Functions
  • Hypergeometric Functions
  • Identities
  • Information Science
  • Lagrangian Functions
  • Notation
  • Partial Differential Equations
  • Power Series
  • Terminals
  • Triangles

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis