Governing Equations of Motion

  • Thomas H. Dawson


In the previous chapter, we considered certain geometric concepts associated with the motion of a continuous medium. We now wish to consider the set of mechanical laws that are customarily assumed to govern the actual continuum motion. These laws express the well-known mechanical principles of conservation of mass, balance of linear momentum, and balance of angular momentum.


Angular Momentum Linear Momentum Momentum Balance Stress Vector External Torque 
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Selected Reading

  1. Malvern, L. E., Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Englewood Cliffs, New Jersey, 1969. Chapters 3 and 5 give detailed discussions of stress and governing continuum equations. Section 5.3 also provides a discussion of the governing equations referred to material coordinates rather than to spatial coordinates, as employed here.Google Scholar
  2. Frederick, D., and T. S. Chang, Continuum Mechanics. Allyn and Bacon, Boston, Massachusetts, 1965. Chapter 2 provides a discussion of stress and Chapter 4 gives a concise derivation of the local forms of mass conservation and momentum balance.Google Scholar
  3. Fung, Y. C., Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey, 1965. Chapters 3 and 5 give thorough discussions of stress and conservation and balance laws.Google Scholar
  4. Long, R. R., Mechanics of Solids and Fluids. Prentice-Hall, Englewood Cliffs, New Jersey, 1961. Chapter 2 introduces the concept of stress and provides an elementary derivation of the local forms of the balance of linear and angular momentum.MATHGoogle Scholar
  5. Truesdell, C., and R. A. Toupin, “The Classical Field Theories,” in Encyclopedia of Physics, Vol III/l. Springer-Verlag, Berlin, 1960. Chapter B discusses conservation of mass and Chapter D presents the general theory of momentum.Google Scholar
  6. Truesdell, C., Essays in the History of Mechanics. Springer-Verlag, Berlin, 1968. Beautifully written essays on the early history of mechanics and the development of its general principles.MATHGoogle Scholar

Copyright information

© Plenum Prees, New York 1976

Authors and Affiliations

  • Thomas H. Dawson
    • 1
  1. 1.United States Naval AcademyAnnapolisUSA

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