Delay Equations and Radiation Damping
arXiv:gr-qc/0101122 · doi:10.1016/S0375-9601(01)00327-9
Abstract
Starting from delay equations that model field retardation effects, we study the origin of runaway modes that appear in the solutions of the classical equations of motion involving the radiation reaction force. When retardation effects are small, we argue that the physically significant solutions belong to the so-called slow manifold of the system and we identify this invariant manifold with the attractor in the state space of the delay equation. We demonstrate via an example that when retardation effects are no longer small, the motion could exhibit bifurcation phenomena that are not contained in the local equations of motion.
15 pages, 1 figure, a paragraph added on page 5; 3 references added
References in corpus (9)
- TIDAL AND TIDAL-RESONANT EFFECTS IN COALESCING BINARIES
- Gravitational radiation reaction and balance equations to post-Newtonian order
- Constructing a Mass-Current Radiation-Reaction Force For Numerical Simulations
- Gravitational Ionization: A Chaotic Net in the Kepler System
- Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation
- Chaos in the Kepler System
- Sustained resonance: a binary system perturbed by gravitational radiation
- Chaos in the Hill system
- Regular order reductions of ordinary and delay-differential equations
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