2 resultados para Choruses, Secular.

em DRUM (Digital Repository at the University of Maryland)


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In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

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The problem was to determine whether a method of aural and visual vocal training that included a program of portable electronic piano keyboard experience would be more effective in teaching sight-singing skills to novice high school chorus students than a method that included only aural and visual vocal training. A sub-problem was to determine whether novice chorus students enjoyed playing electronic keyboards in chorus as a reinforcement experience in sight-singing training. Students were randomly assigned to two treatment groups, tested with the Musical Aptitude Profile, Tonal Imagery, part A, and then trained separately. The experimental group sang repetitions of melodic patterns and utilized techniques associated with the Kodály Method while simultaneously playing keyboard. The comparison group received a similar treatment without using keyboards. The students were pre- and post-tested in sight-singing using the Vocal Sight-Reading Inventory. Results of the Analysis of Covariance using MAP scores as the covariate revealed no significant difference (p<.05) between post-test scores of the two groups. Improvement was noted in 96% of students from pre-test to post-test regardless of grouping. The repeated measures ANOVA revealed a significant relationship (p<.006) between aptitude group and post-test score. High aptitude students in both groups were found to benefit more from the training than low aptitude students. High aptitude keyboard group students achieved an average gain score that was 8.67 points higher than the comparison group. Of the total experimental group, 92% enjoyed playing keyboards in chorus. It is recommended that future research be undertaken to study the use of keyboards with advanced high school choruses and with uncertain singers in the high school chorus. Research is also needed to develop graded, valid, and reliable sight-singing tests for use in high school chorus. Techniques of the Kodály Method should be further investigated for use in high school sight-singing training.