Canonical planetary perturbation equations for velocity-dependent forces, and the Lense-Thirring precession (Q1311446)

A form of planetary perturbation theory based on canonical equations of motion, rather than on the use of osculating orbital elements, is developed and applied to several problems. It is proved that, with appropriately selected initial conditions on the orbital elements, the two forms of perturbation theory give rise to identical predictions for the observable coordinates and velocities, while the orbital elements themselves may be strikingly different. Differences between the canonical form of perturbation theory and the classical Lagrange planetary perturbation equations are discussed. The canonical form of the planetary perturbation equations are derived and applied to the Lense-Thirring precession of a test body in a Keplerian orbit around a rotating mass source.