6,507 research outputs found

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

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    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

    The effect of wave conditions and surfer ability on performance and the physiological response of recreational surfers.

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    This study investigated the effects of wave conditions on performance and the physiological responses of surfers. After institutional ethical approval 39 recreational surfers participated in 60 surfing sessions where performance and physiological response were measured using global positioning system (GPS) heart rate monitors. Using GPS, the percentage time spent in surfing activity categories was on average 41.6, 47.0, 8.1, and 3.1% for waiting, paddling, riding, and miscellaneous activities, respectively. Ability level of the surfers, wave size, and wave period are significantly associated with the physiological, ride, and performance parameters during surfing. As the ability level of the surfers increases there is a reduction in the relative exercise intensity (e.g., average heart rate as a percentage of laboratory maximum, rpartial = -0.412, p < 0.01) which is in contrast to increases in performance parameters (e.g., maximum ride speed (0.454, p < 0.01). As the wave size increased there were reductions in physiological demand (e.g., total energy expenditure rpartial = -0.351, p ≤ 0.05) but increases in ride speed and distance measures (e.g., the maximum ride speed, 0.454, p < 0.01). As the wave period increased there were increases in intensity (e.g., average heart rate as a percentage of laboratory maximum, rp = 0.490, p < 0.01) and increases in ride speed and distance measures (e.g., the maximum ride speed, rpartial = 0.371, p < 0.01). This original study is the first to show that wave parameters and surfer ability are significantly associated with the physiological response and performance characteristics of surfing

    The Golden Channel at a Neutrino Factory revisited: improved sensitivities from a Magnetised Iron Neutrino Detector

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    This paper describes the performance and sensitivity to neutrino mixing parameters of a Magnetised Iron Neutrino Detector (MIND) at a Neutrino Factory with a neutrino beam created from the decay of 10 GeV muons. Specifically, it is concerned with the ability of such a detector to detect muons of the opposite sign to those stored (wrong-sign muons) while suppressing contamination of the signal from the interactions of other neutrino species in the beam. A new more realistic simulation and analysis, which improves the efficiency of this detector at low energies, has been developed using the GENIE neutrino event generator and the GEANT4 simulation toolkit. Low energy neutrino events down to 1 GeV were selected, while reducing backgrounds to the 10410^{-4} level. Signal efficiency plateaus of ~60% for νμ\nu_\mu and ~70% for νˉμ\bar{\nu}_\mu events were achieved starting at ~5 GeV. Contamination from the νμντ\nu_\mu\rightarrow \nu_\tau oscillation channel was studied for the first time and was found to be at the level between 1% and 4%. Full response matrices are supplied for all the signal and background channels from 1 GeV to 10 GeV. The sensitivity of an experiment involving a MIND detector of 100 ktonnes at 2000 km from the Neutrino Factory is calculated for the case of sin22θ13101\sin^2 2\theta_{13}\sim 10^{-1}. For this value of θ13\theta_{13}, the accuracy in the measurement of the CP violating phase is estimated to be ΔδCP35\Delta \delta_{CP}\sim 3^\circ - 5^\circ, depending on the value of δCP\delta_{CP}, the CP coverage at 5σ5\sigma is 85% and the mass hierarchy would be determined with better than 5σ5\sigma level for all values of δCP\delta_{CP}
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