The relativistic generalization of the Chaplygin gas, put forward by Jackiw
and Polychronakos, is derived in Duval's Kaluza-Klein framework, using a u
niversal quadratic Lagrangian. Our framework yields a simplified proof of t
he field-dependent Poincare symmetry. Our action is related to the usual Na
mbu-Goto action [world volume] of d-branes in the same way as the Polyakov
and the Nambu action are in string theory.