  We extend a recent analysis of gravitational perturbations on
Dirac-Nambu-Goto strings, membranes and higher dimensional branes. In an
arbitrary gauge, it is shown that the relevant first order equations governing
the displacement vector of the worldsheet and metric perturbation are
obtainable from a variational principle whose Lagrangian is constructed as a
second order perturbation of the standard Dirac-Goto-Nambu action density. A
symplectic current functional is obtained as a by-product that is potentially
useful for the derivation of conservation laws in particular circumstances.
