O método da média para equações diferenciais não autônomas

Abstract

Based on the papers Geodesics on vibrating surfaces and curvature of the normal family, by Mark Levi and Qiran Ren, and Geometry and physics of averaging with applications, by Mark Levi, we present the averaging method. This allow to study time periodic nonautonomus ordinay diferential equations using autonomous diferential equations with errors that can be controled at given precision. Following the ideas of Mark Levi and Qiran Ren in Geodesics on vibrating surfaces andcurvature of the normal family, we use the averaging method to prove that a normal and periodic vibration of a surface induces on a mass moving freely on it, a tangencial acceleration to the surface. This acceleration is proportional to the curvature of the normal curve.