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Title: Oscillators: Old and new perspectives

We consider some of the well known oscillators in literature which are known to exhibit interesting effects of nonlinearity. We review the Lindstedt-Poincare technique for dealing with with the nonlinear effects and then go on to introduce the relevance of the renormalization group for the oscillator following the pioneering work of Chen et al. It is pointed out that the traditional Lindstedt-Poincare and the renormalization group techniques have operational connections. We use this to find an unexpected mode softening in the double pendulum. This mode softening prompted us to look for chaos in the double pendulum at low energies-energies that are just sufficient to allow the outer pendulum to rotate (the double pendulum is known to be chaotic at high energies-energies that are greater than that needed to make both pendulums to rotate). The emergence of the chaos is strongly dependent on initial conditions.
Authors:
 [1] ;  [2]
  1. Harish-Chandra Research Institute, Jhunsi, Allahabad 211019 (India)
  2. UM-DAE Centre for Excellence in Basic Sciences, Santa Cruz(E), Mumbai 400098 (India)
Publication Date:
OSTI Identifier:
22263917
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1582; Journal Issue: 1; Conference: International conference on complex processes in plasmas and nonlinear dynamical systems, Gandhinagar (India), 6-9 Nov 2012; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; MECHANICAL VIBRATIONS; NONLINEAR PROBLEMS; OSCILLATIONS; OSCILLATORS; RENORMALIZATION; TIME MEASUREMENT