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.

The Oud Across Arabic Culture

This study is a compilation and compendium of information on the oud, the most important instrument in Arabic classical music. It has grown out of my own long-time involvement in studying and playing the oud, and in particular out of my interest in the lack of sources and knowledge available to the vast majority of oud players and researchers, as well as for the readers. My own path started from an intensive study of the oud, which included exposure to several treaties; some housed in museums around the globe, and some only available in the Arabic language. The study combines archival research (including Arabic poetry and pre-Islamic Era and medieval treaties), symbolism, new archaeological discoveries, field interviews, and analysis of existing scholarship, and draws on my professional performance experience for detailed stylistic analysis of the oud's performance practice and its historical development. The study consists of participant observation, personal performance, and interviews conducted in person, via telephone, and/or via e-mail, according to the choice of the performers. The performers have been selected from networks of musicians who perform regularly at lounges, concert halls, and private events. These performers have been chosen according to their musical knowledge, technical skill, experience, and activity in Arabic music and oud performance. Chapter one deals with the purpose of this study and the methods of investigation, as well as giving a brief overview of the history of the oud. In addition, there will be an introduction to the Arabic musical system (mâqâm), which is primarily based on the mechanics and sound production of the oud. Chapter two deals with the oud in Arabic sources: the first source is Arabic poetry in the pre-Islamic Era. The second source is Arabic poetry in the medieval era, in which I found a significant number of poets who allude to the oud, providing accurate descriptions of the player, singers, and the scenes within the contexts of oud performance. The third source is the Arab scholars' intensive treatises with meticulous accounts of the instrument's apparatii, including descriptions and measurements of the parts, strings, and tuning. While chapter three deals with the classification, the development of the oud, chapter four deals with topics such as: the symbolism of the oud and its relation to cosmology, astronomy, mathematics and anatomy. In most of the pertinent Arabic writings, philosophers mention a significant correlation between the oud and the other sciences. Chapter five deals with recreating the performance practice of the oud. A case study of the oud performers focuses on their style, technique, training, and personal experiences. Topics such as improvisation and ornamentation, the oud in the Arabic musical ensemble, the social uses and functions, and gender in musical performance practices will be included in detailed analysis. Other important topics will be analyzed such as traditional vs. modern technique, and the repertoire of the oud. Specifically, in regard to technique, the study outline the style of the music, the role of the oud in Arabic ensembles, the function of the oud in music composition, and the form of the ensembles in Arabic performance and practice.