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2868 results in Solid mechanics and materials

Page 86 of 144

  • 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.

Page 86 of 144