Abstract
The nonlinear gyrokinetic Vlasov equation is derived for an arbitrary magnetized plasma in a local reference frame moving with the nonuniform equilibrium fluid velocity u(r). The derivation of the guiding‐center and gyrocenter Hamilton equations, which appear as the characteristics of the gyrokinetic Vlasov equation, is based on the use of Lie‐transform perturbation techniques. Although a general form for u is initially used, attention is later focused on an incompressible toroidal equilibrium flow when considering axisymmetric tokamak geometry.