Two fundamental problems of celestial mechanics are considered: the stellar or planetary three-body problem and a related form of the restricted four-body problem. Although a number of constraints are imposed, no assumptions are made which could invalidate the final solution. A consistent and rational approach to the analysis of four-body systems has not previously been developed, and an attempt is made here to describe problem evolution in a systematic manner. In the particular three-body problem under consideration two masses, forming a close binary system, orbit a comparatively distant mass. A new literal, periodic solution of this problem is found in terms of a small parameter e, which is related to the distance separating the binary system and the remaining mass, using the two variable expansion procedure. The solution is accurate within a constant error O(e¹¹) and uniformly valid as e tends to zero for time intervals 0(e¹⁴). Two specific examples are chosen to verify the literal solution, one of which relates to the sun-earth-moon configuration of the solar system. The second example applies to a problem of stellar motion where the three masses are in the ratio 20 : 1 : 1. In both cases a comparison of the analytical solution with an equivalent numerically-generated orbit shows .close agreement, with an error below 5 percent for the sun-earth-moon configuration and less than 3 percent for the stellar system. The four-body problem is derived from the three-body case by introducing a particle of negligible mass into the close binary system. Unique uniformly valid solutions are found for motion near both equilateral triangle points of the binary system in terms of the small parameter e, where the primaries move in accordance with the uniformly-valid three-body solution. Accuracy, in this case, is Q maintained within a constant error 0(e⁸), and the solutions are uniformly valid as e tends to zero for time intervals 0(e¹¹). Orbital position errors near L₄ and L₅ of the earth-moon system are found to be less than 5 percent when numerically-generated periodic solutions are used as a standard of comparison. The approach described here should, in general, be useful in the analysis of non-integrable dynamic systems, particularly when it is feasible to decompose the problem into a number of subsidiary cases. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Since no lean body mass (LBM) index was available for women, the purpose of the present study was to use the formula of Behnke et al. in the calculation of an LBM Index for women.

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Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This study grew out of the general problem area concerning the relationship between psychological factors and response to pain. The specific variable focused upon was body image, broadly defined as a constellation of body attitudes and ways of experiencing the body, two of which -- body anxiety and body boundary definiteness -- were studied intensively. Body anxiety, defined as the degree of concern, conflict or anxiety a person experiences about his body, was measured by the Homonym Test, developed by Secord. This is a word association test involving 75 words which can have either a body or a non-body meaning such as "graft" or "colon". Two general measures of anxiety, theTaylor Manifest Anxiety Scale and Holtzman's adaptation of the Elizur Content Anxiety Scale, were also administered. The second body image variable, body boundary definiteness, was defined as an index of a person's sense of differentiation from the world as a separate, intact entity. It was further considered to be an index of the development of differentiated ego boundaries, reflecting highly developed ego-functioning, and consequently, the capacity to modulate response to stress. In order to measure body boundary definiteness, the barrier score of Fisher and Cleveland was used. This score is based on an analysis of inkblot responses emphasizing protective, containing or concealing features. Three aspects of response to pain were studied; these were pain perception, pain tolerance, and adaptation to pain. Operationally, pain perception was measured in terms of the intensity at which an electric shock to the forearm was judged as "uncomfortable" and the level at which it was judged as "painful ". Pain tolerance was likewise measured in two ways. The first, "unmotivated tolerance level", was the point at which subjects first refused to receive higher intensities of shock. The second, "motivated tolerance level", was the point at which subjects refused to go higher following mild urging to go as high as they possibly could. Finally, adaptation to pain was measured in terms of the amount of increase in each of the pain perception and tolerance levels as a result of repeating the level setting procedure following a period of repeated shocks. The specific hypotheses tested in the study were: 1) Definiteness of body boundaries is positively correlated with pain perception threshold. 2) Body anxiety is negatively correlated with pain perception threshold. 3) Definiteness of body boundaries is positively correlated with ability to tolerate pain. 4) Body anxiety is negatively correlated with ability to tolerate pain. 5) Definiteness of body boundaries is positively correlated with adaptation to pain. 6) Body anxiety is negatively correlated with adaptation to pain. The results, based on a sample of 30 subjects, supported only hypotheses one and three, those involving body boundary definiteness. There were significant correlations between the Barrier scores and painful level, unmotivated tolerance level, and motivated tolerance level. The hypothesized relationship between body anxiety and pain perception and pain tolerance were not supported by the experimental results. Neither of the body image variables was correlated with adaptation to pain as stated in hypotheses five and six. This was seen to be the result of the fact that most of the subjects were highly stable in their judgements about pain and in their ability to tolerate pain. Thus, adaptation did not occur. In addition, it was found that the Holtzman Content Anxiety scores were negatively correlated with the two pain tolerance measures. There was a tendency toward an inverted-U shaped relationship between tvlanifest Anxiety and pain perception level and motivated tolerance level. The results of the study were considered to provide partial support for the assumption that body image variables are relevant to response to pain. / 2999-01-01

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