Resonant and Secular Orbital Interations

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.

FLUTE MUSIC FROM THE MID-TWENTIETH CENTURY BY THREE FRENCH COMPOSERS: JEAN-MICHEL DAMASE, ANDRE JOLIVET, AND HENRI TOMASI

Jean-Michel Damase (b.1928), Andre Jolivet (1905-1974), and Henri Tomasi (1901-1971) are three prominent French composers ofthe twentieth century. Tomasi won the Prix de Rome in 1927, and Damase won the Prix de Rome in 1947. All three composers were educated and lived in Paris around the same period; however, their musical styles are quite distinct. Most of Jolivet's compositions for flute are well known and are often selected as international competition repertoire. The compositions for flute by Damase and Tomasi are not as recognized as those of Jolivet, and most of their works for flute still have not been commercially recorded. The purpose of this dissertation is to provide a more comprehensive guide to the compositions for flute by Damase, Jolivet and Tomasi, and, in addition, to make the works ofDamase and Tomasi familiar to flutists. This dissertation will focus on the compositions ofDamase, Jolivet, and Tomasi for flute alone and those for flute and piano, written between 1928 and 1971 (1928 is the year Damase was born, and 1971 is the year that Tomasi died). Damase continues French romanticism, and his music is always playful, elegant, and accessible with rhythmic and harmonic surprises, but with an underlying complexity. His compositions for flute include three concertos, two double concertos, one flute solo work, and nine works for flute and piano. Jolivet's compositions make use of ancient rituals, incantations, and spirituality, as well as repeated phrases and single notes, irregular rhythmic patterns, dissonant effects, and rhythmic drive. He composed one flute concerto, three works for flute solo, and four works for flute and piano. Tomasi's compositions also continue French romanticism and contain melodies which often seem to tell a story, and which are not only full of flourishes and vitality, but are also delicate, colorful, and romantic. Virtuosic technical demand is another characteristic of his style. Tomasi composed three flute concertos, three works for solo flute, and one work for flute and piano. Appendix I is a list of the compositions for flute by Damase, Jolivet, and Tomasi, and Appendix II is a discography of their works.