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Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1369–1374 | Cite as

Renewal of basic laws and principles for polar continuum theories (VI) — Conservation laws of mass and inertia

  • Dai Tian-min
Article

Abstract

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization.

Key Words

polar continua coupled transport theorem conservation law of mass and inertia 

Chinese Library Classification number

O33 

2000 Mathematics Subject Classification

74A35 74A60 

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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Dai Tian-min
    • 1
  1. 1.Department of Mathematics & Center for the Application of MathematicsLiaoning UniversityShenyangP. R. China

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