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.

SAXOPHONE SONATAS 1980-2010

The purpose of this dissertation project identifies contemporary solo saxophone literature, specifically sonatas between the years 1980 and 2010. The overwhelming majority of repertoire written during these thirty years consisted primarily of either multi-movement or through-composed character pieces. By limiting the selected repertoire to sonatas one can still investigate the breadth of the literature that has helped validate the saxophone in the realm of classical music in a format that has seemingly fallen out of favor with composers. The saxophone had developed a unique voice by the middle of the twentieth century in both Europe and in the United States. European composers such as Claude Debussy, Florent Schmidt, Jacques Ibert, Darius Milhaud, Alexander Glazounov, Erwin Schulhoff and Bernard Heiden recognized the potential and beauty of the instrument, while the saxophone had found quite a different niche in vaudeville, jazz, and military bands in the United States. If not for the dynamic performances by concert saxophonist such as Marcel Mule, Sigurd Rascher, Jean-Marie Londeix, Daniel Deffayet, Cecil Lesson, Larry Teal, Eugene Rousseau, Fredrick Hemke and Donald Sinta, the timbral possibilities and technical virtuosity of the saxophone would not have been discovered. The awe inspiring performances by these soloists led to the commissioning of a multitude of works by composers looking to expand the sonic possibilities of this relatively new instrument. Through the 1970's American composers such as Leslie Bassett, Paul Creston, Henry Brant, Robert Muczynski, and Karel Husa were writing significant works for the saxophone, while European composers such as IngolfDahl, Edison Denisov, Alfred Desenclos, Henri Tomasi and Marius Constant were each making their own contributions, all leading to a significant quantity of repertoire that met the quality demands set by the performers. The compositions chosen for this dissertation project were selected after numerous performance, pragmatic, programming and pedagogical considerations were taken into account. The three recitals occurred on: March 7, 2010, December 10, 2010 and May 1, 2011 in either the Gildenhorn Recital Hall or Lecture Hall 2100.