Abstract
In this chapter the classical relativistic formulation of physical laws is analyzed. We begin by recalling the fundamental principles of classical mechanics, since the great revolution produced by special and general relativity cannot be fully appreciated without a complete understanding of the ideas of classical physics.
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Notes
- 1.
Part of the contents of this chapter can be found in Chap. 12 of [143].
- 2.
See [115] and Sect. 7.3.
- 3.
From now on, we drop the lexical distinction between observer and frame of reference associated with an observer, i.e., we identify the observer with the adopted frame of reference.
- 4.
Notice that in prerelativistic mechanics, the “time” plays, from a mathematical point of view, the role of a parameter.
- 5.
See, for instance, [143, Chap. 22].
- 6.
In particular, one of the two particles could be at rest in I.
- 7.
For a historical account of the notion of reference frame, see, for example, [9, 10].
- 8.
The reader interested in classical continuum mechanics can refer to the books [45, 67, 94, 144, 145, 166–168, 177].
- 9.
From now on, uppercase indices are used to identify quantities defined in \(C_{0}\), and lowercase indices specify quantities in C.
- 10.
This is not convenient in classical fluid mechanics.
- 11.
For a proof of this formula, see, for example, [145].
- 12.
The components of \(\nabla \mathbf{v}\) in the Cartesian coordinates \(x_{k}\) are \((\nabla \,\mathbf{v})_{kl}=v_{l, k}\).
- 13.
See, for instance, [144].
- 14.
A volume \(c(t)\subseteq C(t)\) is material if during the motion, S contains the same quantity of matter.
- 15.
See, for instance, [144].
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Romano, A., Mango Furnari, M. (2019). Review of Classical Mechanics and Electrodynamics. In: The Physical and Mathematical Foundations of the Theory of Relativity. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-27237-1_5
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DOI: https://doi.org/10.1007/978-3-030-27237-1_5
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