Coordinates and Momenta for Bead-Spring Models

1 Coordinates and Momenta for Bead-Spring Models (DPI, Sects. 11.6 and 15.1) 

We consider polymer models made up of N beads, joined together in some way by springs some examples for TV = 5 are shown in Fig. 1. Various kinds of springs have been used, including the following  

If desired, internal viscosity can be included by incorporating dashpots in parallel with the springs in the mechanical models. However, this introduces nonconservative forces into the problem. To avoid dealing with nonconservative forces, one can use momentum-space averages of the dashpot term as explained in DPL, Eq. 13C.2-2. We know of no molecular theory that can legitimize the use of dashpots in molecular models. 

The beads in the mechanical models are numbered in an arbitrary manner. We let the position vector of bead v with respect to an arbitrary laboratory-fixed 

It is sometimes convenient to introduce position vectors referred to the center of mass  

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