The Forced Pendulum
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.
KeywordsPeriodic Solution Dirichlet Boundary Dirichlet Boundary Condition Force Term Homogeneous Equation
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