THE MATRIZANTS OF THE KEPLERIAN MOTIONS (THE TWO-DIMENSIONAL CASE)

Abstract

The variational equations of the problem of two bodies have been solved from first principles applying Jacobi's dual theorem of the last multiplier to the adjoint of the Hamiltonian system expressed in Cartesian coordinates with respect to an arbitrarily given inertial frame of reference. Once the matrizant R(t;t0) in that system has been obtained in closed form, other forms of the resolvent are derived simply by homogeneous canonical extensions. By way of illustration, we have recovered in this way the matrizants in the orbital frame of reference and in Hill's intrinsic coordinate system.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1967
Accession Number
AD0663679

Entities

People

  • Andre Deprit

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Angular Momentum
  • Cartesian Coordinates
  • Celestial Mechanics
  • Computers
  • Coordinate Systems
  • Differential Equations
  • Displacement
  • Equations
  • Equations Of Motion
  • Hamiltonian Functions
  • Identities
  • Integrals
  • Linear Differential Equations
  • Orbits
  • Scientific Research
  • Two Dimensional
  • Variational Equations

Readers

  • Control Systems Engineering.
  • Linear Algebra

Technology Areas

  • Space
  • Space - Orbital Debris