In this master thesis, it is proposed to solve in the large thedifferential equationZ2(d2y/dz2) + z (dy/dz) (b0+b1zm) + (c0+c1zm)y = 0Here, m is an arbitrary positive integer, the variable z is complex as are the constants bi, ci (i = 0, 1). It is also assumed that the roots of the indicial equation about the regular singular point z=0 are such that their difference is incongruent to zero modulo m.

Linearized equations of motion are important in engineering applications, especially with respect to stability analysis and control design. Traditionally, the full, nonlinear equations are formed and then linearized about the desired equilibrium configuration using methods such as Taylor series expansions. However, it has been shown that the quadratic form of the Lagrangian function can be used to directly linearize the equations of motion for discrete dynamical systems. Here, this development is extended to directly generate linearized equations of motion for both continuous and hybrid dynamical systems, where a hybrid system is described with both discrete and continuous generalized coordinates. The results presented require only velocity level kinematics to form the Lagrangian and find equilibrium configuration(s) for the system. A set of partial derivatives of the Lagrangian are then computed and used to directly construct the linearized equations of motion about the equilibrium configuration of interest. This study shows that the entire nonlinear equations of motion do not have to be generated in order to construct the linearized equations of motion. Several examples are presented to illustrate application of these results to both continuous and hybrid system problems.

Thesis (M.S.)--University of Missouri, School of Mines and Metallurgy, 1931. / The entire thesis text is included in file. Typescript and handwritten by author. Illustrated by author. Title from title screen of thesis/dissertation PDF file (viewed December 3, 2009) Includes bibliographical references (p. 25) and index (p. 26).

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1928. / "Sonderdruck aus "Mathematische Annalen", Bd. 101, Heft 1"--T.p. verso. Vita. Includes bibliographical references.

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1927. / "Sonderabdruck aus der "Mathematischen Zeitschrift", Band 27, Heft 1"--T.p. verso. Vita. Includes bibliographical references.

Thesis (Ph. D.)--Kent State University, 2008. / Title from PDF t.p. (viewed Nov. 10, 2009). Advisor: Hassan Allouba. Keywords: stochastic partial differential equations; compact support property. Includes bibliographical references (p. 30).

Thesis (M.A..)--Marshall University, 2009. / Title from document title page. Includes abstract. Document formatted into pages: contains 95 pages. Includes bibliographical references p. 94-95.

Thesis (Ph. D.)--West Virginia University, 2003. / Title from document title page. Document formatted into pages; contains ix, 118 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 115-118).

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