The Untangling Transformation

Details The Untangling Transformation The Untangling Transformation

Nov 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005aj....130.2415h&link_type=abstract

The Astronomical Journal, Volume 130, Issue 5, pp. 2415-2417.

Astronomy and Astrophysics

Astronomy

10

Key Word: Celestial Mechanics

Scientific paper

It is always possible to find canonical forms for quadratic Hamiltonians. In cases in which the eigenvalues of the associated linear system are simple, either real or pure imaginary, the canonical form introduces action-angle coordinates that are most useful for the application of perturbation theory; this is the case in which the quadratic Hamiltonian is the first term in the expansion of a nonlinear Hamiltonian around an equilibrium. The general theory is rather involved, and it may be worthwhile to find shortcuts in simple situations. We present here such a shortcut for a quadratic Hamiltonian of 2 degrees of freedom with a symmetry that is often present in celestial mechanics. The canonical transformation proposed has the added advantage of having a clear geometric interpretation and of being a generalization of the so-called reducing transformation that has been useful in several problems.

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