The Forced Pendulum

Robert F. Brown
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Robert F. Brown: University of California, Department of Mathematics

Chapter 5 in A Topological Introduction to Nonlinear Analysis, 2004, pp 29-38 from Springer

Abstract: Abstract The rest of Part I will be devoted to demonstrating the usefulness of two of the tools we have developed: the Schauder fixed point theorem and a compactness property of C k -spaces that is a consequence of the Ascoli-Arzela theorem. We used information from the Ascoli-Arzela and Schauder theories in Chapter 1, to prove the Cauchy-Peano theorem by topological methods. In this chapter, we will illustrate the use of these tools by showing how they establish the existence of solutions to a differential equation problem that comes up in the study of the pendulum.

Keywords: Periodic Solution; Dirichlet Boundary; Dirichlet Boundary Condition; Force Term; Homogeneous Equation (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8124-1_5

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