On Systems of Ordinary, Non-Linear Differential Equations Involving Periodic Given Functions With a Small Period (Classic Reprint) - Hardcover
Synopsis
Explore how periodic inputs shape nonlinear differential systems with a rigorous, paper‑and‑pencil approach that ties theory to concrete estimates.
This book develops an averaging framework for ordinary differential equations where the right‑hand side depends on a small period and shows how time averages lead to smoother, easier‑to‑analyze problems.
The author builds the theory step by step, starting from Lipschitz conditions and integral formulations, then proving key lemmas and a central existence theorem. Throughout, two themes recur: how to craft practical bounds and how to relate a complex, time‑varying system to a simpler averaged version that preserves essential behavior. An included example illustrates the method on a moving‑particle model, highlighting how estimates translate into concrete statements about displacement and velocity.- How periodic forcing and small periods affect nonlinear systems of ODEs
- How to construct and bound time‑averaged functions and their Lipschitz properties
- How integral equations relate to differential equations and how existence/uniqueness is established
- Practical techniques for estimating key quantities such as p(t) and the time horizon T
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On Systems of Ordinary, NonLinear Differential Equations Involving Periodic Given Functions With a Small Period Classic Reprint
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