On Pfaff's equations of motion in dynamics; Applications to satellite theory
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 EulerLagrange 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 twobody 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.
 Publication:

Celestial Mechanics
 Pub Date:
 October 1978
 DOI:
 10.1007/BF01230161
 Bibcode:
 1978CeMec..18..207B
 Keywords:

 Artificial Satellites;
 Astrodynamics;
 Canonical Forms;
 Equations Of Motion;
 EulerLagrange Equation;
 Pfaff Equation;
 Celestial Mechanics;
 Hill Method;
 Perturbation Theory;
 Transformations (Mathematics);
 Two Body Problem;
 Astronomy