  We show that complete cotangent lifts of vector fields, their decomposition
into vertical representative and holonomic part provide a geometrical framework
underlying Eulerian equations of continuum mechanics. We discuss Euler
equations for ideal incompressible fluid and Vlasov equations of plasma
dynamics in connection with the lifts of divergence-free and Hamiltonian vector
fields, respectively. As a further application, we obtain kinetic equations of
particles moving with the flow of contact vector fields both from Lie-Poisson
reductions and with the techniques of present framework.
