The subject of Continuum mechanicsContinuummechanics begins by dealing with the nonrelativistic classical dynamics of continuous deformable media. Examples are oscillations of stretched strings, heat conductionHeatconduction in rods, elastic motion of solidsElastic solid (rods/beams), motion of fluids (air, water) and plasmasPlasma (ionized gases)Gasionized, in roughly increasing order of complexity. All of these systems involve a very large number of moleculesMolecule (or degrees of freedom), and we will treat them as continuous mass/charge distributions with an infinite number of degrees of freedomDegrees of freedominfinite. Thus, unlike particle mechanics, continuum mechanics deals with fields (see Appendix B ). Examples of fields include the height of a stretched string, temperature, elastic displacement, mass density, velocity, pressure, internal energy, specific entropy, charge density, current density, and electric and magnetic fields. While a classical point particle is somewhere at any given time, a classical fieldField is everywhere at any given instant! Thus, continuum mechanics is a collection of (primarily nonrelativistic, classical) field theories. ElectromagnetismElectromagneticfield and gravitationGravitationalfield are other examples of field theories, though they often involve relativistic and/or quantum effects.

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Dynamics of Continuous Deformable Media

  • Govind S. Krishnaswami

摘要

The subject of Continuum mechanicsContinuummechanics begins by dealing with the nonrelativistic classical dynamics of continuous deformable media. Examples are oscillations of stretched strings, heat conductionHeatconduction in rods, elastic motion of solidsElastic solid (rods/beams), motion of fluids (air, water) and plasmasPlasma (ionized gases)Gasionized, in roughly increasing order of complexity. All of these systems involve a very large number of moleculesMolecule (or degrees of freedom), and we will treat them as continuous mass/charge distributions with an infinite number of degrees of freedomDegrees of freedominfinite. Thus, unlike particle mechanics, continuum mechanics deals with fields (see Appendix B ). Examples of fields include the height of a stretched string, temperature, elastic displacement, mass density, velocity, pressure, internal energy, specific entropy, charge density, current density, and electric and magnetic fields. While a classical point particle is somewhere at any given time, a classical fieldField is everywhere at any given instant! Thus, continuum mechanics is a collection of (primarily nonrelativistic, classical) field theories. ElectromagnetismElectromagneticfield and gravitationGravitationalfield are other examples of field theories, though they often involve relativistic and/or quantum effects.