Abstract
A distinctive feature of the mechanical systems we have discussed so far is that their number of degrees of freedom is finite and hence countable. The mechanics of deformable macroscopic media goes beyond this framework. The reaction of a solid state to external forces, the flow behavior of a liquid in a force field, or the dynamics of a gas in a vessel cannot be described by means of finitely many coordinate variables. The coordinates and momenta of point mechanics are replaced by field quantities, i.e. functions or fields defined over space and time, which describe the dynamics of the system.
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One shows, furthermore, that the charge Q is a Lorentz invariant quantity, i.e., that its valuedoes not depend on the frame of reference in which it is calculated. This holds if and only if\(\partial _\mu j^\mu (x) = 0\).
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Scheck, F. (2018). Continuous Systems. In: Mechanics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55490-6_7
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DOI: https://doi.org/10.1007/978-3-662-55490-6_7
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