On the rotation of a molecule near a solid.

This work is a study of the nature of the motion of a molecule near the surface of a solid. The dynamics of some simple models are analysed in detail but these models are too simple to represent a scattering experiment. So the conclusions are qualitative. A method of presenting the global dynamics of a conservative classical system is described. This method is used to present the motion of a rigid rotator colliding with a plane passive surface. Part of the motion on repulsive pair-potentials is interpreted using perturbations from an averaging approximation and part by comparing the motion with that of a dumbell striking a hard wall. Where the potential has a deep well or there is an abrupt change in the force on the molecule the motion of the rotator has no perturbation part. If the motion of a dumbell striking a hard wall is averaged over the initial orientation of the dumbell the transition probabilities are controlled by the bounds due to conserved variables. Some ideas of ergodic theory are considered to find how the strongly-coupled motion might be described. These ideas have bean developed for bound systems and so do not give a unique description of the scattering. Although it is not possible to characterise any system the motion of a dumbell striking a hard wall may be described simply. A quantum formalism to calculate transition probabilities for a dumbell or an ellipsoid striking a plane hard wall is developed. The variations with total energy of these probabilities are interpreted using the classical motion and properties of the quantum equations.