  We develop a new approach to local nonlinear effects in cosmic microwave
background anisotropies, and discuss the qualitative features of these effects.
New couplings of the baryonic velocity to radiation multipoles are found,
arising from nonlinear Thomson scattering effects. We also find a new nonlinear
shear effect on small angular scales. The full set of evolution and constraint
equations is derived, including the nonlinear generalizations of the radiation
multipole hierarchy, and of the dynamics of multi-fluids. These equations
govern radiation anisotropies in any inhomogeneous spacetime, but their main
application is to second-order effects in a universe that is close to the
Friedmann models. Qualitative analysis is given here, and quantitative
calculations are taken up in further papers.
