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8126 results in Fluid dynamics and solid mechanics

Page 200 of 407

  • 19 - Forces and Moments. Balance Laws for Linear and Angular Momentum

  • 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 131-145

  • Summary

    The current entrenched, facile conception of force in terms of “pushes” and “pulls” has fostered a view of force as a “real quantity” rather than a mathematical concept. In the words of Pierce (1934, p. 262): [Force is] “the great conception which, developed in the early part of the seventeenth century from the rude idea of a cause, and constantly improved upon since, has shown us how to explain all the changes of motion which bodies experience, and how to think about physical phenomena; which has given birth to modern science; and which … has played a principal part in directing the course of modern thought … It is, therefore, worth some pains to comprehend it.”

    Those who believe the notion of force is obvious should read the scientific literature of the period following Newton. Truesdell (1966) notes that “D'Alembert spoke of Newtonian forces as ‘obscure and metaphysical beings, capable of nothing but spreading darkness over a science clear by itself,’” while Jammer (1957, pp. 209, 215) paraphrases a remark of Maupertis, “we speak of forces only to conceal our ignorance,” and one of Carnot, “an obscure metaphysical notion, that of force.”

    Within the framework of continuum mechanics, the basic balance laws for linear and angular momentum assert that, given any spatial region Pt convecting with the body,

    1. (i) the net force on Pt is balanced by temporal changes in the linear momentum of Pt;

    2. (ii) the net moment on Pt is balanced by temporal changes in the angular momentum of Pt.

  • PART V - BASIC THERMODYNAMICAL 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 181-182

  • Summary

    In introducing basic versions of the first two laws of thermodynamics appropriate to continua, we emphasize that

    • like force, we view energy, entropy, heat flow, and entropy flow as primitive objects;

    • a priori notions of “equilibrium” and “state” are not employed.

    We find it most convenient to use a spatial formulation–that is, a formulation in terms of quantities measured per unit volume and area in the observed space.

Page 200 of 407