rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Strong Nonlinear Oscillators
    sub title: Analytical Solutions
  name:
    name part: Cveticanin, Livija.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 2nd ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 317 p. 93 illus., 21 illus. in color. online resource.
  abstract: This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author's original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force wh…
  table of contents: Preface to Second Edition -- Introduction -- Nonlinear Oscillators -- Pure Nonlinear Oscillator -- Free Vibrations -- Oscillators with Time-Variable Parameters -- Forced Vibrations -- Harmonically Excited Pure Nonlinear Oscillator -- Two-Degree-of-Freedom Oscillator -- Chaos in Oscillators -- Vibration of the Axially Purely Nonlinear Rod.
  note: by Livija Cveticanin.
  subject:
    topic: Vibration
  subject:
    topic: Dynamical systems
  subject:
    topic: Dynamics
  subject:
    topic: Physics
  subject:
    topic: Mathematical physics
  subject:
    topic: Statistical physics
  subject:
    topic: Vibration, Dynamical Systems, Control
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Mathematical Applications in the Physical Sciences
  subject:
    topic: Applications of Nonlinear Dynamics and Chaos Theory
  classification: TA355
  classification: TA352-356
  classification: 620
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Mathematical Engineering
  identifier: 9783319588261
  identifier: https://doi.org/10.1007/978-3-319-58826-1
  record info:
    record creation date: 170529
    record change date: 20191025011909.0
    record identifier: 978-3-319-58826-1