Existence of invariant volumes in nonholonomic systems

We derive sufficient conditions for a nonholonomic system to preserve a smooth volume form; these conditions become necessary when the density is assumed to only depend on the configuration variables. Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. This result is applied to the Suslov problem for left-invariant systems on Lie groups (where the underlying space is Poisson rather than symplectic).Comment: 29 pages, 3 figure

High-resolution Elemental Mapping of the Lunar Surface

New instruments and missions are being proposed to study the lunar surface as a result of the resurgence of interest in returning to the Moon. One instrument recently proposed is similar in concept to the x-ray fluorescence detectors flown on Apollo, but utilizes fluorescence from the L- and M-shells rather than the K-shell. This soft X-Ray Flourescence Imager (XRFI) is discussed