Balance Laws

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The basic laws of mechanics can all be expressed, in general, in the following form, $$ \frac{d}{{dt}}\int\limits_{Pt} {\psi dv = \int\limits_{\partial Pt} {{\phi _\psi }nda + \int\limits_{Pt} {{\delta _\psi }dv} } } $$ (2.1) , for any bounded regular subregion of the body, called a part P ⊂ B and the vector field n, the outward unit normal to the boundary of the region Pt in the current configuration. The quantities Ψ and σΨ are tensor fields of certain order m, and σΨ is a tensor field of order m + 1, say m = 0 or m = 1, so that σ is a scalar or vector quantity, and, respectively, σΨ is a vector or second-order tensor quantity.KeywordsInertial FrameTensor FieldLinear MomentumJump ConditionReference ConfigurationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.