The problems associated with the modification of Hamilton's principle to cover nonholonomic constraints by the application of the multiplier theorem of variational calculus are discussed. The reason for the problems is subtle and is discussed, together with the reason why the proper account of nonholonomic constraints is outside the scope of Hamilton's variational principle. However, linear velocity constraints remain within the scope of D'Alembert's principle. A careful and comprehensive analysis facilitates the resolution of the puzzling features of nonholonomic constraints.

Highlights of these investigations are: 1. We defined, formulated and developed the concept of a classical inelastic form factor. 2. By appeal to the dynamical SO(4) symmetry of H{n, i), we were able to provide the first exact classical and quantal solutions for the Stark Mixing problem for the whole array of nl-n'V transitions in Rydberg atoms. This has been a long outsi anding problem in Atomic Physics for the past 40 years. 3. By exploiting the classical form factor, we were able to formulate the first classical impulse theory for nl-> n'V collisional transitions in Rydberg atoms. In this paper a new way of formulating the quantal impulse approximation is presented which allows one to obtain its classical limit in a natural and rather simple way. The presented approach which involves the Wigner functions of initial and final states exhibits in a lucid way the quantitative relationship between this quantum impulse approximation and the binary encounter approach. So far this connection has been rather obscure. As far as inelastic collisions are concerned, the presented results have a great potential in inspiring new semiclassical approaches. In my t5pinion,the main result of this paper is of topical significance in two respects. Firstly, the quantal impulse approximation is of central importance in general scattering theory. Secondly, recently there has been a general strong interest in the power of classical dynamics and in its connection with quantum dynamics (Compare with Refs. 10-15). As a minor remark, in this context it might be worth not only to refer to time-independent problems but also to some semiclassical work dealing with explicitly time dependent problems (e.g. G. Alber and 0. Zobay, PRA 59, R3174 (1999)). Futher-more, the presentation of the material is clear and scientifically sound. I recommend publication." 4. In a referee report on paper #4, "Quantal Stark Mixing at ultralow energies", J. Phys. B: Atom. Mol. Opt. Phys. 33 (2000) L721, the referee wrote: "The article presents an elegant derivation, based on group theoretical arguments, of angular mixing transition probabilities between t and I' states in hydrogen induced by low energy collisions with charged particles..." 5. In a referee report on paper #5 "Classical Stark mixing at ultralow collision energies", Phys. Rev. Letts, 85, (2000), 4880, the referee wrote: _ "The paper presents an elegant solution to a long-standing problem in atomic physics, but the method of approach is of interest to a much wider community because the authors show how to exploit the classical/quantum correspondence in a system with a rich dynamical symmetry. It is rare to find so comprehensive a solution to a difficult problem...." 6. In a referee report on paper #6, Analytical quantal collisional Stark Mixing Probabilities , J. Phys. B: At. Mol. Opt. Phys. 34 (2001), LI, the referee writes: "The authors present interesting analytical and numerical results on collision-induced Stark mixing probabilities for hydrogen and, more generally, for Rydberg atoms. These re...

The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Q j of each polar atom. Analytical expressions are obtained for all Q j associated with principal quantum number n of H(n) and permit the longrange expansion for the H(n)-H(n) first-order interaction to be explicitly expressed analytically in terms of n, n and internuclear distance R. Possible quasi-molecular formation is investigated. Direct calculations show that the H(n = 2)-H(n = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.