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We examine the origin of dynamical friction using a non-perturbative,orbit-based approach. Unlike the standard perturbative approach, in whichdynamical friction arises from the LBK torque due to pure resonances, thisalternative, complementary view nicely illustrates how a massive perturbersignificantly changes the energies and angular momenta of field particles onnear-resonant orbits, with friction arising from an imbalance between particlesthat gain energy and those that lose energy. We treat dynamical friction in aspherical host system as a restricted three-body problem. This treatment isapplicable in the `slow' regime, in which the perturber sinks slowly and thestandard perturbative framework fails due to the onset of non-linearities.Hence it is especially suited to investigate the origin of core-stalling: thecessation of dynamical friction in central constant-density cores. We identifythree different families of near-co-rotation-resonant orbits that dominate thecontribution to dynamical friction. Their relative contribution is governed bythe Lagrange points (fixed points in the co-rotating frame). In particular, oneof the three families, which we call Pac-Man orbits because of their appearancein the co-rotating frame, is unique to cored density distributions. When theperturber reaches a central core, a bifurcation of the Lagrange pointsdrastically changes the orbital make-up, with Pac-Man orbits becoming dominant.In addition, due to relatively small gradients in the distribution functioninside a core, the net torque from these Pac-Man orbits becomes positive(enhancing), thereby effectuating a dynamical buoyancy. We argue that corestalling occurs where this buoyancy is balanced by friction.

Dynamical Friction, Buoyancy and Core-Stalling -- I. A Non-perturbative Orbit-based Analysis