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8126 results in Fluid dynamics and solid mechanics

Page 203 of 407

  • 20 - Frames of Reference

  • from PART IV - BASIC MECHANICAL PRINCIPLES
  • Morton E. Gurtin, Carnegie Mellon University, Pennsylvania, Eliot Fried, McGill University, Montréal, Lallit Anand, Massachusetts Institute of Technology
  • Book:
    The Mechanics and Thermodynamics of Continua
    Published online:
    05 June 2012
    Print publication:
    19 April 2010, pp 146-156

  • Summary

    According to Truesdell & Noll (1965, §41): “The position of an event can be specified only if a frame of reference, or observer, is given. Physically, a frame of reference is a set of objects whose mutual distances change comparatively little in time, like thewalls of a laboratory [or] the fixed stars … Only if such a frame is given for all times does it make sense to compare the positions of a particle at different times, and only then can we speak about velocities, accelerations, etc. of a particle …”

    Changes of Frame

    As noted in section (5.2), Bt is the region actually observed during the motion: The reference body B serves only to label material points. For that reason, to discuss a notion of invariance under observer changes, it is useful to differentiate conceptually between the ambient space for B and the space through which Bt evolves (Figure 20.1). In accord with this:

    1. (i) the ambient space through which Bt evolves is termed the observed space;

    2. (ii) the ambient space for the reference body B is termed the reference space.

    Granted this dichotomy, spatial vectors belong to the observed space, while material vectors belong to the reference space.

    Suppose that a frame of reference F for the observed space is prescribed, an assumption tacit in the discussion thus far. Then, roughly speaking, a change of frame is, at each time, a rotation and translation of the observed space.

Waves and Mean Flows
  • Oliver Bühler
  • Published online:
    29 March 2010
    Print publication:
    20 August 2009
  • Interactions between waves and mean flows play a crucial role in understanding the long-term aspects of atmospheric and oceanographic modelling. Indeed, our ability to predict climate change hinges on our ability to model waves accurately. This book gives a modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. A detailed account of the theory of linear dispersive waves in moving media is followed by a thorough introduction to classical wave–mean interaction theory. The author then extends the scope of the classical theory and lifts its restriction to zonally symmetric mean flows. The book is a fundamental reference for graduate students and researchers in fluid mechanics, and can be used as a text for advanced courses; it will also be appreciated by geophysicists and physicists who need an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science.

Solitons
  • P. G. Drazin
  • Published online:
    25 March 2010
    Print publication:
    21 July 1983
  • A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.

Acoustics of Fluid-Structure Interactions
  • M. S. Howe
  • Published online:
    22 March 2010
    Print publication:
    13 August 1998
  • Acoustics of Fluid-Structure Interactions addresses an increasingly important branch of fluid mechanics - the absorption of noise and vibration by fluid flow. This subject, which offers numerous challenges to conventional areas of acoustics, is of growing concern in places where the environment is adversely affected by sound. Howe presents useful background material on fluid mechanics and the elementary concepts of classical acoustics and structural vibrations. Using examples, many of which include complete worked solutions, he vividly illustrates the theoretical concepts involved. He provides the basis for all calculations necessary for the determination of sound generation by aircraft, ships, general ventilation and combustion systems, as well as musical instruments. Both a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is an important synthesis of information in this field. It will also aid engineers in the theory and practice of noise control.

Analytical Dynamics
  • A New Approach
  • Firdaus E. Udwadia, Robert E. Kalaba
  • Published online:
    22 March 2010
    Print publication:
    23 February 1996
  • Constrained motion is of paramount importance in the design and analysis of mechanical systems and central to the study of analytical dynamics. The problem of constrained motion was first posed over two hundred years ago, and it has been worked on vigorously ever since. This book offers a fresh approach to the subject. Eminently readable, it is written as an introduction to analytical dynamics, with emphasis on fundamental concepts in mechanics. The connection between generalized inverses of matrices and constrained motion is a central theme. The book begins with a description of the motion of a particle subjected to holonomic and nonholonomic constraints and presents explicit equations of motion. Examples are provided throughout the book, and carefully formulated problems at the end of each chapter reinforce the material covered. This computationally appealing approach will be useful to students in engineering and the applied sciences.

Page 203 of 407