Celestial mechanics

, Volume 18, Issue 3, pp 207–222 | Cite as

On Pfaff's equations of motion in dynamics; Applications to satellite theory

  • R. Broucke
Article
Received:

Abstract

In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered.

Keywords

Velocity Component Canonical Transformation Satellite Theory Canonical Equation True Anomaly 
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Copyright information

© D. Reidel Publishing Company 1978

Authors and Affiliations

  • R. Broucke
    • 1
  1. 1.Department of Aerospace Engineering and Engineering MechanicsUniversity of TexasAustinUSA

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