Applied Mathematics and Mechanics (English Edition) ›› 2006, Vol. 27 ›› Issue (2): 167-174 .doi: https://doi.org/10.1007/s10483-006-0204-y

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RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ) —MASTER BALANCE LAW

戴天民   

  • 收稿日期:2004-04-04 修回日期:2005-11-12 出版日期:2006-02-18 发布日期:2006-02-18
  • 通讯作者: 戴天民

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ) —MASTER BALANCE LAW

DAI Tian-min   

  1. Department of Mathematics & Center for the Application of Mathematics, Liaoning University, Shenyang 110036, P.R. China
  • Received:2004-04-04 Revised:2005-11-12 Online:2006-02-18 Published:2006-02-18
  • Contact: DAI Tian-min

Abstract: Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether's theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energy-momentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.

Key words: unified master balance law, physical field quantities, conservation laws, energy-momentum, energy-angular momentum, energy-energy

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