Dissertation--Hamburg--Universität der Bundeswehr, 2001. / Bibliogr. p. 245-254.

An integral of motion is a function of the states of a dynamical system that is constant along the system’s trajectories. Integrals are known for their utility as a means of reducing the dimension of a system, effectively leaving only one differential – or in some cases algebraic – equation to be solved. Invariants of dynamical systems have also proven useful in other contexts, such as in estimation, numerical integration and optimal control. Regardless of the manner in which an integral is employed, finding an analytic form for the integrals of a system generally requires solution of a system of non-linear partial differential equations, with the exception of cases in which certain symmetries of the system are apparent. The objective of this work is to investigate a generalized method for determining motion integrals for non-linear dynamical systems. This method will not work for all nonlinear systems. Indeed, it is expected that the results will test the limitations of this method. In this we consider a method for determining integrals of motion for a small class of dynamical systems akin to the traditional series expansion method for solving partial differential equations. This method involves posing a candidate integral of motion as a series expansion in terms of some set of polynomials. The coefficients of the candidate polynomial are treated as the unknowns in a system of equations. The system of equations is constructed by sampling simulated trajectories of the dynamical system in question. Then the coefficients are solved for using singular value decomposition. There are a number of parameters that can potentially affect this method’s ability to generate an integral of motion that effectively approximates the phase space of the full nonlinear dynamical system. Part of this thesis proposes what some of these parameters might be and investigates how they affect the outcome. A couple of well-known systems are used to conduct these tests: the simple pendulum and the rotating rigid body. The simple pendulum is one of the simplest examples of a non-linear system, and examples of the rotating rigid body in aerospace engineering are ubiquitous.

Thesis (M.A.)--University of Hawaii at Manoa, 2004. / Includes bibliographical references (leaves 111-121). / ix, 121 leaves, bound ill., map 29 cm

Precision cosmology challenges many aspects of fundamental physics. In particular, quasar absorption lines test the assumed constancy of fundamental constants over cosmological time-scales and distances. Until recently, the most reliable technique was the alkali doublet (AD) method where the measured doublet separation probes variations in the fine-structure constant, ???? e2/??c. However, the recently introduced many-multiplet (MM) method provides several advantages, including a demonstrated ???10-fold precision gain. This thesis presents detailed MM analyses of 3 independent Keck/HIRES samples containing 128 absorption systems with 0.2 &gt zabs &gt 3.7. We find 5.6 ?? statistical evidence for a smaller ?? in the absorption clouds: ????/?? = (-0.574 ?? 0.102) x 10-5. All three samples separately yield consistent, significant ????/??. The data marginally prefer constant d??/dt rather than constant ????/??. The two-point correlation function for ?? and the angular distribution of ????/?? give no evidence for spatial variations. We also analyse 21 Keck/HIRES Si iv doublets, obtaining a 3-fold relative precision gain over previous AD studies: ????/?? = (-0.5 ?? 1.3) x 10-5 for 2.0 &gt zabs &gt 3.1. Our statistical evidence for varying ?? requires careful consideration of systematic errors. Modelling demonstrates that atmospheric dispersion is potentially important. However, the quasar spectra suggest a negligible effect on ????/??. Cosmological variation in Mg isotopic abundances may affect ????/?? at zabs &gt 1.8. Galactic observations and theory suggest diminished 25;26Mg abundances in the low metallicity quasar absorbers. Removing 25;26Mg isotopes yields more negative ????/?? values. Overall, known systematic errors can not explain our results. We also constrain variations in y ?? ?? 2gp, comparing H i 21-cm and millimetrewave molecular absorption in 2 systems. Fitting both the H i and molecular lines yields the tightest, most reliable current constraints: ??y/y = (-0.20??0.44)x10-5 and (-0.16??0.54)x10-5 at zabs = 0.2467 and 0.6847 respectively. Possible line-ofsight velocity differences between the H i and molecular absorbing regions dominate these 1 ?? errors. A larger sample of mm/H i comparisons is required to reliably quantify this uncertainty and provide a potentially crucial check on the MM result.

Thesis (Ph. D.)--University of New South Wales, 2002. / Also available online.

Diss. : Sprach- und Literaturwissenchaft : Duisburg : 1980. - Bibliogr. p. 251-262. -

Thesis (doctoral)--Vereinigte Friedrichs-Universität Halle-Wittenberg, 1913. / Vita.

Thesis (Ph. D.)--Columbia University. / "Books of reference": p. 1-8.

Thesis (Ph.D.)--York University, 2009. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 219-222). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR51680

Thesis (Ph.D.)--Columbia University. / "Books of reference": p. 1-8.