Abstract
While physical variables describe the quantitative attributes of physical systems, the equations linking them describe the quantitative behaviour of phenomena, i.e. the physical laws. We will distinguish four kinds of equations used in physics, and for each kind we put into evidence their mathematical structure. The main classification is that of defining equations, topological equations, equations of behaviour and phenomenological equations.
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Notes
- 1.
We remember that those global variables which are associated with an extended space element, such as a line, a surface or a volume, coincide with integral variables, i.e. are obtained by integration of the field functions. But there are also global variables associated with points, and these cannot be integral variables; see pp. 106 and 110.
- 2.
In Chap. 9 we will show that the relation p = m  v is not the definition of momentum but a constitutive law, whereas momentum is, by definition, the indefinite time integral of force.
- 3.
Post [185, p. 291].
- 4.
Truesdell and Toupin [237, p. 227].
- 5.
Demirel [54, p. 6].
- 6.
This was the first constitutive equation in history; see Truesdell [237, p. 702].
- 7.
- 8.
- 9.
See the list of physical variables on p. 485.
- 10.
Topological equations can be described by algebraic topology using cochains, also called discrete forms, and the coboundary operator. In the differential setting, they can be described by scalar- or vector-valued exterior differential forms and by an exterior differential.
- 11.
- 12.
See Chap. 10 for the experimental apparatus.
- 13.
Pauli [174, pp. 20–21].
- 14.
See the next chapter.
- 15.
See page 161.
- 16.
- 17.
Truesdell and Toupin [237, p. 233].
References
Benvenuto, E.: An Introduction to the History of Structural Mechanics, Part I, p. 274. Springer, Dordrecht, The Netherlands (1991)
Born, M.: Kritische Betrachtungen zur traditionellen Darstellung der Thermodynamik. Zeitschrift fur Physik. XXII, 218–224 (1921)
Demirel, T.: Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical & Biological Systems. Elsevier Science, Amsterdam (2002)
Faraday, M.: Remarks on Static Induction. Proceedings of the Royal Institution, 12 Feb 1858
Gordon, J.E., Wagley, S.: The Science of Structures and Materials, vol. 23. Scientific American Library/Scientific American Books, New York (1988)
Guggenheim, E.A.: Termodinamica. Einaudi, Turin, Italy (1952)
Pauli, W.: Elettrodinamica. Bollati Boringhieri, Turin, Italy (1964)
Post, E.J.: Magnetic symmetry, improper symmetry and Neumann’s principle. Found. Phys. 8(3/4), 277–294 (1978)
Schelkunoff, S.A.: Electromagnetic Fields. Blaisdell, New York (1963)
Truesdell, C., Toupin, R.: The Classical Field Theories. Encycl. Phys. III(1) (1960) [Springer, Berlin]
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Tonti, E. (2013). Analysis of Physical Equations. In: The Mathematical Structure of Classical and Relativistic Physics. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7422-7_6
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