Transition to the Normal Modes

According to speculations in Chapter 3 (see Section 3.2), the standard equation of macromolecular dynamics can be written in the form 

The external resistance force of a particle in equation (7.1) is split into two terms, the first of which is equal to ((v,J — v3i r ) - the resistance in a corresponding monomer liquid, and the second one, T) , is connected with the neighbouring macromolecules and satisfies the equation, which can be written in the simplest covariant form (see Section 8.4 and Appendix D). 

Similarly, the internal resistance force Gf satisfies the covariant-form equation / c C1a  

The matrices Hf and G 7 describe the mutual influences of the particles of the chain and depend not only on the direction of particle motion in comparison with direction of chain in the vicinity of the particle labelled a (the local anisotropy) (see equation (3.13)), but also on the mean anisotropy of the medium (the global anisotropy). 

Equations (7.2) and (7.3) determine the covariant expressions for the external and internal resistance forces, which, in linear approximation, can be written as expressions (3.6) and (3.7), respectively. We may notice that to obtain a more general linear form of equations for forces, the terms 7uFf and 7uGf multiplied by arbitrary constants which, nevertheless, could depend on the mode number, should be added to the left-hand side of equations (7.2) and (7.3) respectively. Then, after having calculated the results, the arbitrary quantities can be estimated on the basis of certain requirements (Pyshnograi 1997). However, further on we shall proceed with expressions (7.2) and (7.3), for simplicity s sake. 

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