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The dynamics of compact binary systems at the fourth post-Newtonian (4PN)approximation of general relativity has been recently completed in aself-consistent way. In this paper, we compute the ten Poincar\'e constants ofthe motion and present the equations of motion in the frame of the center ofmass (CM), together with the corresponding CM Lagrangian, conserved energy andconserved angular momentum. Next, we investigate the reduction of the CMdynamics to the case of quasi-circular orbits. The non local (in time) taileffect at the 4PN order is consistently included, as well as the relevantradiation-reaction dissipative contributions to the energy and angularmomentum.

Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order