The Classical Mechanics of Mode-Mode Energy Flow in Polyatomic Molecules

Energy flow can occur among all vibrational modes and rotational motion of a polyatomic molecule. The flow is made possible by various types of couplings between these components. For example, vibrational couplings, whose effects are independent of molecular rotations, may allow for energy flow between vibrational modes. Coriolis coupling in a rotating molecule can provide an additional pathway for the same. Finally, anharmonicities in the modes may also affect the flow of energy. This thesis is about the effects of these two couplings and of mode anharmonicity on two normal vibrational modes of equal harmonic frequencies. The treatment is restricted to classical mechanics. Four models with different combinations of couplings and mode anharmonicities are studied. In general, such models are non-integrable, rendering a rigorous analysis impossible. They are simplified by taking advantage of a nonlinear resonance through the method of secular perturbations. With no further approximations, closed form solutions for the energy flow can be found for each of the four models. These are provided with a physical interpretation. A limited comparison with trajectories, solved numerically, of the original model is performed.