Adiabatic mass amplitude

Only for t > r do we have the right to expect that the shock wave amplitude will approach the self-similar value which we have found. Due to the adiabatic character of the motion, the entropy of the mass m0 always remains constant, and differs from the value which is obtained by extrapolation of the self-similar entropy distribution to this mass. 

Clearly, the assets of a useful, in itself noncontradictory, and physically based CNM analysis are the internal vibrational motions and their properties as well as the amplitudes that relate internal modes to normal modes. As shown in the previous section, the adiabatic internal modes an are the appropriate candidates for internal modes. Adiabatic modes are based on a dynamic principle, they are calculated by solving the Euler-Lagrange equations, they are independent of the composition of the set of internal coordinates to describe a molecule, and they are unique in so far as they provide a strict separation of electronic and mass effects [18,19]. Therefore, they fulfil the first requirement for a physically based CNM analysis. 

---