Swinging Spiral Arms
  We study transient spiral structures in an isothermal, thin, galactic disc.
We find no instability that can grow everywhere from infinitesimal
disturbances, but spiral structure does grow in the disc due to an arbitrarily
strong, asymmetric, central source. An initially finite spiral undergoes
transient swing amplification as it is gradually wound-up by differential
rotation. An independent sequence in negative time describes a leading spiral
swinging to a trailing spiral. The dynamical coupling is established between
the swinging potential and the arm particles, by ensuring that this potential
constrains a locally rotating distribution function centred on the arms. This
swing amplification propagates in radius at the constant rotational speed of
the disc, and leaves behind an exponential density decline in space and time.
