Reciprocal vectors dynamical projection

By repeating the reasoning applied in Section VI to the dynamical reciprocal vectors, we may confirm that any vectors so defined will satisfy Eqs. (2.186)-(2.189). It will hereafter be assumed that (except for pathological choices of S v) they also satisfy completness relation (2.190). A few choices for the tensors S v and T yield useful reciprocal vectors and projection tensors, for which we introduce special notation ... 

We also define dynamical reciprocal basis vectors that are closely related to the dynamical projection tensor defined above. We define a set off vectors... 

In this section, we introduce generalized definitions of sets of reciprocal basis vectors, and of corresponding projection tensors, which include the dynamical reciprocal vectors and the dynamical projection tensor introduced in Section VI as special cases. These definitions play an essential role in the analysis of the constrained Langevin equation given in Section IX. 

Dynamical reciprocal vectors and m) , which were introduced in Section VI, are defined by taking T = H in Eq. (2.208). The corresponding projection tensor is the dynamical projection tensor P v-... 

The pseudoforce associated with the dynamical projection tensor may be calculated by using dynamical reciprocal vectors to evaluate Eq. (2.205). In the simple case of a coordinate-independent mobility as in a free-draining model or a model with an equilibrium preaveraged mobility, we may use Eq. (A. 17) to express as a derivative... 

---