Certain computations concerning a special case of the three body problem
Series expansion to evaluate periodic solvents ejection paths
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Series expansion to evaluate periodic solvents ejection paths
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Periodic orbits of the asteroidal type in the circular restricted problem are studied by varying the period of the infinitesimal body (asteroid) and the mass ratio of the primaries (Sun-Jupiter mass ratio). The results indicate that asteroidal periodic orbits can exist for the actual Sun-Jupiter mass ratio for resonances of the Hecuba (2:1), Hilda (3:2) and Thule (4:3) groups, but not for resonances of higher consecutive integer ratios. It is also found that an asteroid can be placed in a periodic orbit at a position with mean motion between 2:1 and 3:2 even if Jupiter is about 9 times more massive than its actual value. However, an asteroid cannot be placed in a periodic orbit beyond the 4:3 resonance for the actual Sun-Jupiter mass ratio.
Lunar laser-ranging data, accumulated between 1970 and 1986, are analyzed to estimate the deviation of the precession of the moon's orbit from the predictions of general relativity. No deviation from this predicted de Sitter precession rate of nearly 2 angular sec per century (sec/cy) is found, to within an estimated standard error of 0.04 sec/cy. This standard error, 2 percent of the predicted effect, incorporates an assessment of the likely contributions of systematic errors, and is about threefold larger than the statistical standard error.
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This thesis presents preliminary measurements of the moments of angular distribution for the K?K+ mesonic final state using a quasi-real, linearly polarised photon. Two of the main points of focus for this analysis were the development of the formalism for photoproduced vector-pseudoscalar decay and the tools by which the analysis was carried out. The formalism described how the moments of angular distribution could be extracted from the angular decay variables, and how they related to resonance decays in terms of partial waves. In extracting the moments, it was found that adapted Markov Chain Monte Carlo (MCMC) methods proved to be more effective in terms of extracting results from the data compared to the sole use of gradient descent based fitting algorithms. These measurements are complementary to other decay channels and production mechanisms, with the global aim of probing the existence of exotic mesons. Data from this analysis was taken by the CLAS collaboration at the Thomas Jefferson National Accelerator Facility (JLab) by scattering from a liquid hydrogen target using a 10.6 GeV electron. This work was done within the MesonEx program at CLAS12 that aims to map the spectrum of mesons, and in doing so, gain a greater understanding of Quantum ChromoDynamics (QCD) and the strong force.
Three dimensional elastic body fracture analysis, considering lateral constraint factor contour plots
Generalization of space restricted three-body problem by spinor regularization