Table 1.

Kinematic conserved densities for polytropic equations of state (2.14).

conserved density Tdescriptionnumberexponent
ρmass1γ arbitrary
ρumomentumnγ arbitrary
ρuxangular momentumn(n−1)/2γ arbitrary
ρ(tux)Galilean momentumnγ arbitrary
Embedded Imageenergy1γ≠1
Embedded Imageenergy1γ=1
Embedded Imagesimilarity energy1γ=1+2/n
Embedded Imagedilational energy1γ=1+2/n