The Hamiltonian in the Planetary or Satellite Problem as a D'Alembertian Function

Details The Hamiltonian in the Planetary or Satellite Problem as a D'Alembertian Function The Hamiltonian in the Planetary or Satellite Problem as a D'Alembertian Function

Jul 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001arep...45..577k&link_type=abstract

Astronomy Reports, Volume 45, Issue 7, July 2001, pp.577-579

Astronomy and Astrophysics

Astronomy

Scientific paper

This completes a series of three articles establishing the d’Alembertian properties of key functions in celestial mechanics. The first two presented the concept of a d’Alembertian function of a pair of complex variables specified within an infinitely long bottle with a narrowing neck. The main properties of d’Alembertian functions were demonstrated, and it was shown that the main functions in celestial mechanics belong to this class, including Cartesian coordinates. The d’Alembertian radii of these functions were found and their moduli estimated, in many cases exactly. The current paper demonstrates the d’Alembertian nature of the perturbing function—or equivalently, the Hamiltonian—in the planetary or satellite problem. The d’Alembertian radius of this function is estimated.

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