Hamiltonian G-Spaces with Regular Momenta

Let G be a compact connected non-Abelian Lie group and let (P, w, G, J) be a Hamiltonian G-space. Call this space a G-space with regular momenta if J(P) ⊂ g*reg, here g*reg⊂g* denotes the regular points of the co-adjoint action of G. Here problems involving a G-space with regular momenta are reduced to problems in an associated lower dimensional Hamiltonian T-space, where T ⊂ G is a maximal torus. For example two such G-spaces are shown to be equivalent if and only if they have equivalent associated T-spaces. We also give a new construction of a normal form due to Marle (1983), for integrable G-spaces with regular momenta. We show that this construction, which is a kind of non-Abelian generalization of action-angle coordinates, can be reduced to constructing conventional action-angle coordinates in the associated T-space. In particular the normal form applies globally if the action-angle coordinates can be constructed globally. We illustrate our results in concrete examples from mechanics, including the rigid body. We also indicate applications to Hamiltonian perturbation theory

Dendrobates leucomelas

Number of Pages: 6Integrative BiologyGeological Science

Why Computing? Motivations and Mathematics to Pursue Postsecondary CIS Education

Computing and information sciences (CIS) careers in the United States are expected to grow faster than the average occupation between 2019 and 2029 and educational requirements for these positions span subbaccalaureate and baccalaureate degrees. Despite secondary curricular interventions, the population of people who pursue CIS pathways are not diverse by race, ethnicity, socioeconomic status, or gender. This study applies situated expectancy-value theory to investigate the motivational factors which influence the decision to pursue postsecondary CIS degree programs for students in the High School Longitudinal Study of 2009 (n = 18,730). Prior CIS experiences are associated with increased odds of declaring subbaccalaureate and baccalaureate CIS within three years of high school, but several math-related factors are associated only with pursuing baccalaureate CIS. These results have implications for designing interventions that encourage more students to pursue computing careers and understanding why students choose between two postsecondary educational paths

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem

The propagation of tree seedlings under continuous light in square, bottomless containers

Six woody ornamental species were selected to study the effects of continuous light and square, bottomless containers on growth and development during greenhouse propagation phase and after planting to field or 3-gallon container. Species tested were Liquidambar styraciflua, Koelreuteria paniculata, Betula pendula, Magnolia x soulangeana, Quercus palustris, and Prunus caroliniana. K. paniculata grew tallest when started under continuous light. Continuous light had no effect on caliper, fresh weight, straightness rating, or root rating of K. paniculata. Fresh weight of plants started in bottomless containers was heavier than plants started in containers with bottoms. The root quality rating of K. paniculata seedlings from bottomless container treatments was better than seedlings that were started in containers with bottoms. Continuous light had a positive effect on the height and fresh weight of Magnolia x soulangeana seedlings. Plants from continuous light treatments were more crooked, however. Magnolia x soulangeana grew more in height, caliper, fresh weight, and had better root quality rating when started in bottomless containers. Seedlings of B. pendula started in bottomless containers were taller than those started in containers with bottoms. Bottomless containers also produced plants with greater caliper, fresh weight, and better root quality and straightness rating. Photoperiod treatments had no effect on the growth of B. pendula. B. pendula planted in the field had larger caliper and were heavier than seedlings planted in 3-gallon containers. Liquidambar styraciflua was the most unresponsive species tested to treatments. Photoperiod or container type had no influence on height, caliper, fresh weight, or straightness rating at either growing location. Root quality rating of field plants was better for plants from natural photoperiod treatments. Continuous light and bottomless containers interacted to produce the highest root quality rating of 3-gallon container pi ants. Q. palustris seedlings grew tallest when started under continuous light. Continuous light treatments also produced seedlings with greater fresh weight and root quality ratings. Continuous light had no effect on caliper or straightness rating of Q. palustris. Container type had no effect on height, caliper, fresh weight, or straightness rating. Seedlings started in bottomless containers had better root quality rating. Continuous light treatments produced taller P. caroliniana seedlings but did not influence caliper, fresh weight, straightness or root quality rating. Container type had no effect on height, caliper, fresh weight, or straightness rating of P. caroliniana. Seedlings started in bottomless containers had better root quality ratings than those started in containers with bottoms

An Investigation of the Overlap Between the Statistical Discrete Gust and the Power Spectral Density Analysis Methods

The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected