me863outline_s08 - Outline of the Lecture Notes 1...

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ME 863 Nonlinear Oscillations Spring 2008 Outline of the Lecture Notes: 1. Introduction to Nonlinear Vibration 2. Linearization and local stability Time-variant autonomous systems Local stability of hyperbolic (real parts of eigenvalues are nonzero) fixed point governed by eigenvalues (Rand 1.1; NM 3.2.1) Phase portraits (Rand 1.1) 3. Conservative Systems: Period of Free Vibration Phase portraits, x' vs. x by energy methods (NM 1.2, 2.1-2. .2; Rand 2.0) Elliptic integral method for period (NM 2.2; Rand 2.2) Regular perturbation fails: secular terms (NM 2.3.1) Lindstedt's method: allow frequency to be amplitude dependent (NM 2.3.2; Rand 2.1) Harmonic-balance method (NM 2.3.4) Period indeed is amplitude dependent (NM 2.4; Rand 2.1-2) 4. Limit Cycles Polar coordinates (notes) Hopf bifurcation (Rand 3.2) Multiple scales (two-variable expansion) introduced in analyzing Rayleigh's equation (notes) Averaging: variation of constants viewpoint (Rand 3.1; NM 3.3.4)
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This note was uploaded on 09/29/2009 for the course ME 863 taught by Professor Go during the Spring '09 term at Michigan State University.

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me863outline_s08 - Outline of the Lecture Notes 1...

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