From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Large Area Crop Inventory Experiment (LACIE). Intensive test site assessment report

There are no author-identified significant results in this report

Physiological Profile of Male Competitive and Recreational Surfers

Surfing consists of both high- and low-intensity paddling of varying durations, using both the aerobic and anaerobic systems. Surf-specific physiological studies lack adequate group sample sizes, and V[Combining Dot Above]O2peak values are yet to determine the differences between competitive and recreational surfers. The purpose of this study was therefore to provide a comprehensive physiological profile of both recreational and competitive surfers. This multisite study involved 62 male surfers, recreational (n = 47) and competitive (n = 15). Anthropometric measurements were conducted followed by dual-energy x-ray absorptiometry, anaerobic testing and finally aerobic testing. V[Combining Dot Above]O2peak was significantly greater in competitive surfers than in recreational surfers (M = 40.71 ± 3.28 vs. 31.25 ± 6.31 ml·kg·min, p \u3c 0.001). This was also paralleled for anaerobic power (M = 303.93 vs. 264.58 W) for competitive surfers. Arm span and lean total muscle mass was significantly (p ≤ 0.01) correlated with key performance variables (V[Combining Dot Above]O2peak and anaerobic power). No significant (p ≥ 0.05) correlations were revealed between season rank and each of the variables of interest (V[Combining Dot Above]O2peak and anaerobic power). Key performance variables (V[Combining Dot Above]O2peak and anaerobic power) are significantly higher in competitive surfers, indicating that this is both an adaptation and requirement in this cohort. This battery of physiological tests could be used as a screening tool to identify an athlete\u27s weaknesses or strengths. Coaches and clinicians could then select appropriate training regimes to address weaknesses

GREAT: the SOFIA high-frequency heterodyne instrument

We describe the design and construction of GREAT, the German REceiver for Astronomy at Terahertz frequencies operated on the Stratospheric Observatory for Infrared Astronomy (SOFIA). GREAT is a modular dual-color heterodyne instrument for highresolution far-infrared (FIR) spectroscopy. Selected for SOFIA's Early Science demonstration, the instrument has successfully performed three Short and more than a dozen Basic Science flights since first light was recorded on its April 1, 2011 commissioning flight. We report on the in-flight performance and operation of the receiver that - in various flight configurations, with three different detector channels - observed in several science-defined frequency windows between 1.25 and 2.5 THz. The receiver optics was verified to be diffraction-limited as designed, with nominal efficiencies; receiver sensitivities are state-of-the-art, with excellent system stability. The modular design allows for the continuous integration of latest technologies; we briefly discuss additional channels under development and ongoing improvements for Cycle 1 observations. GREAT is a principal investigator instrument, developed by a consortium of four German research institutes, available to the SOFIA users on a collaborative basis

Normal-internal resonances in quasi-periodically forced oscillators: a conservative approach

We perform a bifurcation analysis of normal–internal resonances in parametrised families of quasi–periodically forced Hamiltonian oscillators, for small forcing. The unforced system is a one degree of freedom oscillator, called the ‘backbone’ system; forced, the system is a skew–product flow with a quasi–periodic driving with basic frequencies. The dynamics of the forced system are simplified by averaging over the orbits of a linearisation of the unforced system. The averaged system turns out to have the same structure as in the well–known case of periodic forcing ; for a real analytic system, the non–integrable part can even be made exponentially small in the forcing strength. We investigate the persistence and the bifurcations of quasi–periodic –dimensional tori in the averaged system, filling normal–internal resonance ‘gaps’ that had been excluded in previous analyses. However, these gaps cannot completely be filled up: secondary resonance gaps appear, to which the averaging analysis can be applied again. This phenomenon of ‘gaps within gaps’ makes the quasi–periodic case more complicated than the periodic case