Orateur
Description
Non-conservative processes, such as gravitational radiation in
compact binaries, are inherently challenging to describe within traditional
action principles. To address this limitation, a useful strategy is to embed
the system into a higher dimensional manifold, which allows the variational
principle to be reframed via initial (causal) conditions. This approach has
been explored both in quantum settings (the Schwinger-Keldysh formalism),
and in classical settings: Galley's non-conservative principle of stationary
action. Building upon Galley's principle, we present a novel extension of
discrete Hamiltonian mechanics to non-conservative systems. We show that
this framework can systematically recast any second-order system of ordinary
differential equations as a Hamiltonian system, irrespective of prior
canonical structure. In particular, we exploit our formalism by generalizing
the Lie perturbation approach to dissipative systems, and then applying it
to solving the equations of motion for post-Newtonian radiating binaries,
departing from the point-mass ADM Hamiltonian at 2.5PN. This generalized Lie
method allows for a systematic computation of both secular and oscillatory
contributions to inspiral dynamics, holding promise for precision waveform
modelling in next-generation gravitational wave detectors.
