1935/04/01 by Carl Eckart · 8 citations
Chemistry · Mathematics · Physics and Astronomy · #Amplitude #Casimir effect #Chemical Thermodynamics and Molecular Structure #Classical mechanics #Force Microscopy Techniques and Applications #Geometry #Hamiltonian (control theory) #Inertia #Invariant (physics) #Mathematics #Mechanical and Optical Resonators #Molecule #Moment of inertia #Normal coordinates #Normal mode #Physics #Polyatomic ion #Principal axis theorem #Quantum mechanics #Rotation (mathematics) #Rotational energy #Vibration
paper · doi:10.1103/physrev.47.552
openalex publication_date 1935/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14
The theory of small vibrations when the potential energy is invariant under the rotation-displacement group is developed. The results are compared with the Brester-Wigner theory of the normal coordinates, and it is shown that the use of these coordinates implies the use of a particular (normal) system of rotating axes whose construction is given. It is shown that when the motion of a normal molecule is referred to these axes, those terms of the Hamiltonian which are linear in the angular momenta will be especially small and of the same order of magnitude as the quadratic terms (Casimir's condition). When the amplitude of one or more of the normal vibrations becomes large, this is no longer true of the normal axes; this will always be the case when one of the normal frequencies is small compared to the others, as has been noted by other writers. The normal axes are not the principal axes of inertia of the instantaneous configuration of the system, and certain conclusions recently published by the author are wrong for that reason.