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A Lagrangian from which derive the third post-Newtonian (3PN) equations ofmotion of compact binaries (neglecting the radiation reaction damping) isobtained. The 3PN equations of motion were computed previously by Blanchet andFaye in harmonic coordinates. The Lagrangian depends on the harmonic-coordinatepositions, velocities and accelerations of the two bodies. At the 3PN order,the appearance of one undetermined physical parameter \lambda reflects anincompleteness of the point-mass regularization used when deriving theequations of motion. In addition the Lagrangian involves two unphysical(gauge-dependent) constants r'_1 and r'_2 parametrizing some logarithmic terms.The expressions of the ten Noetherian conserved quantities, associated with theinvariance of the Lagrangian under the Poincar\'e group, are computed. Byperforming an infinitesimal ``contact'' transformation of the motion, we provethat the 3PN harmonic-coordinate Lagrangian is physically equivalent to the 3PNArnowitt-Deser-Misner Hamiltonian obtained recently by Damour, Jaranowski andSch\"afer.Comment: 30 pages, to appear in Classical and Quantum Gravit

classical and quantum gravity

Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms