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The equations of motion of nonspinning compact binary systems at the thirdpost-Newtonian (PN) order in massless scalar-tensor theories have recently beenobtained. In the present paper, we complete this work by computing at 3PN orderthe ten integrals of motion together with the equations of motion in thecenter-of-mass frame. We then perform the reduction of the center-of-massequations to quasi-circular orbits and determine the conserved energy andangular momentum for circular orbits.

Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order