IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4757-5867-2_5.html
   My bibliography  Save this book chapter

Oscillations I

In: Modern Analytic Mechanics

Author

Listed:
  • Richard K. Cooper

    (Formerly of Los Alamos National Laboratory)

  • Claudio Pellegrini

    (University of California at Los Angeles)

Abstract

In this chapter we discuss the general problem of the stability of a dynamical system. The problem can be studied by first finding the conditions for the system to be in a state of equilibrium — when all the forces acting on the system balance to zero — and then determining whether the equilibrium is stable or unstable. Near the equilibrium state the system can be described approximately as an ensemble of coupled oscillators, and we can find the characteristic frequencies of oscillations and determine whether the motion of the oscillators is bounded or unbounded. In the first case, we say that the system is in a stable equilibrium state and in the second that is in an unstable equilibrium state. The characteristic frequencies also define the response of the system to additional external forces. This method of studying the stability of a dynamical system and its motion near an equilibrium point is very general, and can be used to study very different dynamical systems, ranging from musical instruments, to a building subject to an earthquake, to molecules, or even to a simple pendulum.

Suggested Citation

  • Richard K. Cooper & Claudio Pellegrini, 1999. "Oscillations I," Springer Books, in: Modern Analytic Mechanics, chapter 0, pages 95-119, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-5867-2_5
    DOI: 10.1007/978-1-4757-5867-2_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4757-5867-2_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.