Density waves in the shearing sheet I. Swing amplification

The shearing sheet model of a galactic disk is studied anew. The theoretical description of its dynamics is based on three building blocks: Stellar orbits, which are described here in epicyclic approximation, the collisionless Boltzmann equation determining the distribution function of stars in phase space, and the Poisson equation in order to take account of the self-gravity of the disk. Using these tools I develop a new formalism to describe perturbations of the shearing sheet. Applying this to the unbounded shearing sheet model I demonstrate again how the disturbances of the disk evolve always into `swing amplified' density waves, i.e. spiral-arm like, shearing density enhancements, which grow and decay while the wave crests swing by from leading to trailing orientation. Several examples are given how such `swing amplification' events are incited in the shearing sheet.