where we introduced here, for every trajectory α and for every nucleus ν, the concepts of velocity, i.e., Ṙα ν (t), of (kinematic) momentum, i.e., P α ν (t), and of force, i.e., F α ν (t). In particular, P α ν (t) and F α ν (t) will be expressed in terms of the TDVP and of the TDPES. The trajectories can be assimilated to a moving grid: while in the quantum treatment the value of a function f (R, t) can be determined at time t at any point R, in the trajectorybased treatment only the values f (R α (t), t) are accessible. Clearly, for a very large number of trajectories N tr , information is not lost when going from the quantum to the trajectorybased treatment. It is important to note that, in order to evaluate how functions of the type f (R α (t), t) evolve, only total time-derivatives can be computed instead of partial timederivatives.