Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Lectures on Mechanics
  • Cited by 219
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      August 2012
      April 1992
      ISBN:
      9780511624001
      9780521428446
      DOI:
      https://doi.org/10.1017/CBO9780511624001
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.4kg, 268 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Fluid Dynamics and Solid Mechanics
      Series:
      London Mathematical Society Lecture Note Series (174)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Fluid Dynamics and Solid Mechanics
    Series:
    London Mathematical Society Lecture Note Series (174)
    Information

    Book description

    The use of geometric methods in classical mechanics has proven to be a fruitful exercise, with the results being of wide application to physics and engineering. Here Professor Marsden concentrates on these geometric aspects, and especially on symmetry techniques. The main points he covers are: the stability of relative equilibria, which is analyzed using the block diagonalization technique; geometric phases, studied using the reduction and reconstruction technique; and bifurcation of relative equilibria and chaos in mechanical systems. A unifying theme for these points is provided by reduction theory, the associated mechanical connection and techniques from dynamical systems. These methods can be applied to many control and stabilization situations, and this is illustrated using rigid bodies with internal rotors, and the use of geometric phases in mechanical systems. To illustrate the above ideas and the power of geometric arguments, the author studies a variety of specific systems, including the double spherical pendulum and the classical rotating water molecule. This book, based on the 1991 LMS Invited Lectures, will be valued by pure and applied mathematicians, physicists and engineers who work in geometry, nonlinear dynamics, mechanics, and robotics.

    Reviews

    "...centres around symmetry and symplectic quotients. Many examples are given illustrating the utility and relevance of symplectic quotients....readable and stimulating." Michael Atiyah, Bulletin of the American Mathematical Society

    "...The virtue [of this book] is in the breadth, relevance, and complexity of the examples treated..." Mathematical Reviews

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents

    Metrics

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.