  We present a set of cosmological variables, called "supercomoving variables,"
which are particularly useful for describing the gas dynamics of cosmic
structure formation. For ideal gas with gamma=5/3, the supercomoving position,
velocity, density, temperature, and pressure are constant in time in a uniform,
isotropic, adiabatically expanding universe. Expressed in terms of these
supercomoving variables, the cosmological fluid conservation equations and the
Poisson equation closely resemble their noncosmological counterparts. This
makes it possible to generalize noncosmological results and techniques to
cosmological problems, for a wide range of cosmological models. These variables
were initially introduced by Shandarin for matter-dominated models only. We
generalize supercomoving variables to models with a uniform component
corresponding to a nonzero cosmological constant, domain walls, cosmic strings,
a nonclumping form of nonrelativistic matter (e.g. massive nettrinos), or
radiation. Each model is characterized by the value of the density parameter
Omega0 of the nonrelativistic matter component in which density fluctuation is
possible, and the density parameter OmegaX of the additional, nonclumping
component. For each type of nonclumping background, we identify FAMILIES within
which different values of Omega0 and OmegaX lead to fluid equations and
solutions in supercomoving variables which are independent of Omega0 and
OmegaX. We also include the effects of heating, radiative cooling, thermal
conduction, viscosity, and magnetic fields. As an illustration, we describe 3
familiar cosmological problems in supercomoving variables: the growth of linear
density fluctuations, the nonlinear collapse of a 1D plane-wave density
fluctuation leading to pancake formation, and the Zel'dovich approximation.
