The Eckart frame Hamiltonians in the three-body problem

The Eckart frame is used to separate out the collective rotations in the quantum three-body problem. Explicit expressions for the corresponding rotational and vibro-rotational (i.e. Coriolis) Hamiltonians are derived. Special attention is paid to the situation when two principal moments of inertia are equal in the equilibrium configuration.Comment: 12 pages, 2 figures. Regular pape

Oriented robot motion planning in Riemannian manifolds

We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length computations. In particular, we show that for large classes of oriented manifolds, e.g. for spin manifolds, the topological complexity of the oriented frame bundle is bounded from below by the dimension of the base manifold.Comment: 18 pages, revised version, to appear in Topology and its Application

Kinetic Inflation in Stringy and Other Cosmologies

An inflationary epoch driven by the kinetic energy density in a dynamical Planck mass is studied. In the conformally related Einstein frame it is easiest to see the demands of successful inflation cannot be satisfied by kinetic inflation alone. Viewed in the original Jordan-Brans-Dicke frame, the obstacle is manifest as a kind of graceful exit problem and/or a kind of flatness problem. These arguments indicate the weakness of only the simplest formulation. {}From them can be gleaned directions toward successful kinetic inflation.Comment: 26 pages, LaTeX, CITA-94-2