The total part of a generalized vector field X on the bundle E -> M is the generalized vector field Y on E -> M such that Y - X is a vertical vector and Hook(Y, omega) = 0 for any contact 1-form omega on J^1(E).

The vertical vector Y - X is called the evolutionary part of the vector field X.

The command TotalVector is part of the DifferentialGeometry:-JetCalculus package.  It can be used in the form TotalVector(...) only after executing the commands with(DifferentialGeometry) and with(JetCalculus), but can always be used by executing DifferentialGeometry:-JetCalculus:-TotalVector(...).