Browsing by Subject "Trajectories"
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Item Automated generation and optimization of ballistic lunar capture transfer trajectories(2009-08) Griesemer, Paul Ricord; Ocampo, CesarThe successful completion of the Hiten mission in 1991 provided real-world validation of a class of trajectories defined as ballistic lunar capture transfers. This class of transfers is often considered for missions to the Moon and for tours of the moons of other planets. In this study, the dynamics of the three and four body problems are examined to better explain the mechanisms of low energy transfers in the Earth-Moon system, and to determine their optimality. Families of periodic orbits in the restricted Earth-Sun-spacecraft three body problem are shown to be generating families for low energy transfers between orbits of the Earth. The low energy orbit-to-orbit transfers are shown to require less fuel than optimal direct transfers between the same orbits in the Earth-Sun-spacecraft circular restricted three body problem. The low energy transfers are categorized based on their generating family and the number of flybys in the reference three body trajectory. The practical application of these generating families to spacecraft mission design is demonstrated through a robust nonlinear targeting algorithm for finding Sun-Earth- Moon-spacecraft four body transfers based on startup transfers indentified in the Earth- Sun three body problem. The local optimality of the transfers is examined through use of Lawden’s primer vector theory, and new conditions of optimality for single-impulse-to-capture lunar transfers are established.Item Database of planar and three-dimensional periodic orbits and families near the moon(2021-08-20) Franz, Carter Joseph; Russell, Ryan Paul, 1976-; Jones, BrandonThe renewed interest in Lunar exploration prompts a need to better understand the dynamics of spacecraft in the vicinity of the moon. Here, a detailed survey is conducted via a broad grid search to find, characterize, and archive periodic orbits. The resulting database contains over 13 million planar and three-dimensional solutions in the circular restricted three body problem. The work is a direct follow-on to previous periodic orbit grid searches, with a focus on the Earth-Moon mass ratio, the addition of x-z symmetric orbits, and family clustering. Each periodic orbit successfully identified is evaluated for stability properties, perilune distance, number and center of revolutions, and other defining properties. DBSCAN, an unsupervised learning clustering algorithm, is used to isolate family curves in phase space and group orbits into family or sub-family clusters. The clustered orbits are then sorted to form smooth, ordered curves in phase space, allowing for arbitrary data resolution and improved labeling of the discrete grid solutions. A custom cluster confidence measure is introduced and applied. Over 80% of 3D data and over 62% of planar data are clustered with high confidence, with better results at lower revolutions. Approximately 4.25% of 3D solutions and less than 0.5% of planar solutions are classified as outliers. The resulting database is an extension of several recent lunar periodic orbit studies, and can be considered a modern update to Broucke's seminal database of planar cislunar periodic orbits. This new public database is a tool for future mission design and has potential use in a variety of catalogue maintenance space situational awareness applicationsItem Trajectories, predictors, and adolescent health outcomes of childhood weight gain : a growth mixture model(2014-12) Bichteler, Anne; Gershoff, Elizabeth T.Obesity, as defined as BMI at or above the 95th percentile on the Centers for Disease Control and Prevention’s growth charts, has increased almost 3-fold among children in the United States since 1980. Overweight in adolescence has been associated with increased fat retention and high blood pressure in adulthood, among other symptoms of metabolic syndrome. However, normative patterns of weight change in childhood have not been developed. Groups of children may follow different trajectory patterns of BMI change over time. If common trajectory patterns could be identified, and their risk factors and outcomes understood, more nuanced intervention with families and children at risk for obesity could be developed. This study used a national dataset of 1,364 children whose weight and length was measured 12 times from birth through 15 ½ years. Testing both latent class growth analysis and growth mixture modeling identified four distinct subgroups, or classes, of BMI growth trajectory from 24 months – 8th grade. These classes were compared on numerous demographic, biological, and psychosocial risk factors identified in previous research as related to obesity. Classes were differentiated primarily on the child’s BMI at 15 months, the mother’s BMI at 15 months, birth weight for age, and percent increase in birth weight. Being male, Black, and lower SES were also related to membership in the higher-BMI trajectory classes. Of the psychosocial factors, maternal sensitivity, maternal depression, and attachment classification were also related to BMI class. Membership in these trajectories strongly predicted weight-related and blood-pressure outcomes at 15 ½ years over and above individual risk factors, demonstrating that patterns of change themselves are highly influential. The best-fitting models of weight-related outcomes at 15 ½ years included change trajectory in combination with biological, psychosocial, and SES risk factors from 0-24 months, with R² ranging from .31 = .50. Characteristics predicting adolescent overweight can be identified in the first years of life and should trigger the development and implementation of early intervention protocols in obstetrics and pediatrics.