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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DAI Tian-min
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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
2010 MSC Number:
O33
74A35
74A60
DAI Tian-min. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ) —MASTER BALANCE LAW. Applied Mathematics and Mechanics (English Edition), 2006, 27(2): 167-174 .
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URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-006-0204-y
https://www.amm.shu.edu.cn/EN/Y2006/V27/I2/167