Analysis of Rotation--Vibration Relative Equilibria on the Example of a Tetrahedral Four Atom Molecule

We study relative equilibria (RE) of a nonrigid molecule, which vibrates about a well-defined equilibrium configuration and rotates as a whole. Our analysis unifies the theory of rotational and vibrational RE. We rely on the detailed study of the symmetry group action on the initial and reduced phase space of our system and consider the consequences of this action for the dynamics of the system. We develop our approach on the concrete example of a four-atomic molecule A4 with tetrahedral equilibrium configuration, a dynamical system with six vibrational degrees of freedom. Further applications and illustrations of our results can be found in [van Hecke et al., Eur. Phys. J. D At. Mol. Opt. Phys., 17 (2001), pp. 13--35].