Governing Equations of Motion
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.
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- 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
- 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
- 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
- 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