A simplified form for the Hamiltonian and Lagrangian of the spin-independent gravitational two-body system
In general, the gravitational two-body Hamiltonian, to order c-2, contains GP2, G (P · r)2, and G2 terms. We have previously shown [4-6] that a proper choice of coordinate system enables one to eliminate the G (P · r)2 term. We now show that, making use of energy conservation, and coordinate transformations, we can eliminate either of the remaining two terms. In particular, we are able to write down a Hamiltonian and a Lagrangian that contain no mixed potential and kinetic terms. © 1976 Plenum Publishing Corporation.
Publication Source (Journal or Book title)
General Relativity and Gravitation
O'connell, R. (1976). A simplified form for the Hamiltonian and Lagrangian of the spin-independent gravitational two-body system. General Relativity and Gravitation, 7 (10), 805-808. https://doi.org/10.1007/BF00778759