Projected tensors inertial projection

The inertial and geometrical projection tensors, and associated reciprocal vectors, are identical for models with equal masses for all beads, in which the mass tensor is proportional to the identity. 

Cartesian kinetic SDEs with unprojected, geometrically projected, and inertially projected random forces require the same correction forces in certain special cases. Inertial and geometric projections are completely equivalent for models with an equal bead mass m for all beads, for which the mass tensor m v = is proportional to the identity. Unprojected and geometrically projected random forces require identical correction forces in the case of local, isotropic friction with an equal friction coefficient for all beads, as in the Rouse or Kramers model, for which the friction tensor ... 

We then compare Eq. (2.418) to the second line on the RHS of Eq. (2.390), for the case of a generalized projection tensor = P , which is the same as the inertial or geometric projection tensor in this simple class of models. After some straightforward algebra, we find that, for the class of models to which Liu s algorithm applies, the last term in Eq. (2.390) may be written more explicitly as... 

---