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.

MUSICAL EXOTICISM EXPLORED IN PIANO WORKS FROM THE EIGHTEENTH CENTURY THROUGH THE EARLY TWENTIETH CENTURY

Musical exoticism is the evocation of a culture different from that of the composer. It occurs anytime a composer tries to conjure up the music of a country not his own. Although there have been studies of exoticism in the piano works of an individual composer, namely Debussy, there has not been a comprehensive study of musical exoticism in the piano literature as a whole. Upon chronological examination of the piano repertoire, general trends exhibiting exoticism become evident. The first general trend is the emergence of the Turkish style (alia turca) in the eighteenth century. Turkish style soon transmuted to the Hungarian-Gypsy style (all 'ongarese or style hongrois). [In Beethoven's Op. 129, it is alia ingharese.] Composers often alternated between the two styles even in the same composition. By the late nineteenth century, style hongrois was firmly entrenched in the musical language of Austro-German composers, as seen in the works of Brahms. In the nineteenth century, composers turned to the Middle East, North Africa and Spain for inspiration. In particular are several compositions emulating Spanish dance music, culminating in the Spanish works of Debussy and Ravel. The gamelans from Indonesia and objects from the Far East of Japan and China, brought by advances in trade and transportation, captivated the imagination of composers at the turn of the twentieth century. Also in the early twentieth century, composers tried emulating dance and jazz music coming from the Americas, such as the cakewalk, minstrelsy, and the blues. One sees the ever widening sphere of exotic inspiration for western music composers: from the Turkish invasions to the traveling Gypsies of Hungary; to the captivating dance rhythms, soulful cante jondo sections, and guitar flourishes of Spain; expanding further to the far reaches of Asia and the jazzy rhythms of the Americas. This performance dissertation consists of three recitals presented at the University of Maryland, and is documented on compact disc recordings which are housed within the University of Maryland Library System. The recordings present the music of Balakirev, Beethoven, Brahms, Chopin, Debussy, Haydn, Hummel, Milhaud, Moszkowski, Mozart, Ravel, and Schubert.

A GOLDEN AGE: FRENCH AND SPANISH CELLO MUSIC FROM SAINT-SAENS TO CASSADO

Motivated by both the delicacy of French music, such as La Mer by Claude Debussy, and the exotic atmosphere of Spanish music, such as Zigeunerweisen by Pablo Sarasate, I decided to investigate the characteristics of French and Spanish cello music from Camille Saint-Saens to Gaspar Cassad6. French cello music flourished from the end ofthel9th to the middle of the 20th century because of the innovation of many unprecedented techniques and experimentation with a variety of sonorities. The Spanish were heavily influenced by the French due to the geographical connection. Cello virtuosi like Auguste Tolbecque, August Franchomme, Pierre Fournier, and Paul Tortelier inspired composers of their day, creating a "golden age" of cello music. This dissertation consisted of three recitals in Gildenhom Recital Hall. The first recital was held on May lOth, 2007 at 5:30pm with pianist David Ballena. The second recital was held on October 14th, 2007 at 2pm with collaborators Minna Han, piano and Jenny Wu, violin. The third recital was held on March 301 2008 at 5:30 with pianist Naoko Takao. Here is the program of the recitals: The first recital: Gabriel Faure(1856-1924): Sonate pour Violoncello et Piano Op.109(1917) Gaspar Cassad6 (1897-1966): Suite per Violoncello Solo (1926) Claude Debussy (1862-1918): Sonate pour Violoncelle et Piano (1915) The second recital: Manuel de Falla (1876-1946): Melodia (1897), Romanza (1898) Camille Saint-Saens (1835-1921): Concerto for Cello and Orchestra No.1 in A minor Op.33 (1873) Maurice Ravel (1875-1973): Sonata for Violin and Cello (1920-22) The third recital: Pablo Casals (1876-1973): Song of the Birds (1925) Edouard Lalo (1823-1892): Concerto for Cello and Orchestra in D Minor (1877) Franscis Poulenc (1899-1963): Sonata for Cello and Piano Op.l43(1940-48)