Density waves in the shearing sheet - I. Swing amplification

The shearing sheet model of a galactic disk is studied anew. The theoretica l description of its dynamics is based on three building blocks: stellar or bits, which are described here in epicyclic approximation, the collisionles s Boltzmann equation determining the distribution function of stars in phas e space, and the Poisson equation in order to take account of the self-grav ity of the disk. Using these tools I develop a new formalism to describe pe rturbations of the shearing sheet. Applying this to tile unbounded shearing sheet model I demonstrate again how the disturbances of the disk evolve al ways into "swing amplified" density Raves, i.e. spiral-arm like, shearing d ensity enhancements, which grow and decay while the wave crests swing by fr om leading to trailing orientation. Several examples are given how such "sw ing amplification" events are incited in the shearing sheet.