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Question : How to eliminate zero frequency rotational and translational modes in small oscillations of molecules?
Translational zero modes
For analyzing the small oscillations of molecules, the authors explain how to eliminate translations and rotations before starting calculations. In solving a mechanical problem of molecular oscillations, it is convenient to eliminate immediately the translational and rotational degrees of freedom.The former can be removed by equating to zero the total momentum of the molecule. Since this condition implies that the centre of mass of the molecule is at rest, it can be expressed by saying that the three co-ordinates of the centre of mass are constant.
Rotational zero modes
To eliminate the rotation of the molecule, its total angular momentum must be equated to zero. Since the angular momentum is not the total time derivative of a function of the co-ordinates, the condition that it is zero cannot, in general, be expressed by saying that some such function is zero. For small oscillations, however, this can in fact be done.
For more details see
Landau L. D. and E. M. Lifshitz , 'Mechanics', 3rd Edition Butterworth-Heineman, Oxford (1993).
