Angle-action variables for orbits trapped at a Lindblad resonance
James Binney
Abstract
ABSTRACT The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasi-periodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.
Topics & Concepts
PhysicsTorusQuasiperiodic functionContext (archaeology)Resonance (particle physics)Orbit (dynamics)Kolmogorov–Arnold–Moser theoremClassical mechanicsGalaxyAstrophysicsAction (physics)Quantum mechanicsGeometryHamiltonian systemCondensed matter physicsEngineeringPaleontologyBiologyMathematicsAerospace engineeringQuantum chaos and dynamical systemsAstro and Planetary ScienceStellar, planetary, and galactic studies