Abstract
This chapter is dedicated to a relatively abstract question: Do balance laws and constitutive equations keep their form if we switch from an observer at rest to an arbitrarily moving one? In mathematical terms this problem can be analyzed by using so-called Euclidean transformations and establish an almost philosophical principle according to which true laws of nature must keep their form, independently of the frame of reference.
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- 1.
For the determinant of Eq. (8.3.1) we could simply write det(O′) = ±1. This is a consequence of Eqs. (8.2.5/8.2.7), which follows from the fact that the inverse of a rotation matrix is given by its transposed. However, there are didactic reasons why we do not write it that way in Eq. (8.3.1): In Chap. 13 we will introduce so-called world tensors in complete analogy to Eq. (8.3.1/8.3.2). However, in contrast to the Euclidean transforms the corresponding world transforms are not normalized.
- 2.
The Latin citations stem from the third edition of Newton’s book and can be found in the most carefully edited two volumes by Koyré et al. [9]. When compared to the first edition of the Principia (1687) we notice considerable differences in the wording, in terms of alterations as well as additional comments. This is an indication of Newton’s lifelong struggle with his findings, and it also shows how his understanding grew steadily over time. Moreover, note, that all but one translation of the original Latin text stem from the book of Chandrasekhar (1995). The translation of the “hypotheses non fingo” passage is from Cohen and Whitman (1999).
- 3.
Strictly speaking Thirring’s analysis also allows the hollow sphere to rotate with an angular velocity different from ω.
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Müller, W.H. (2014). Observers and Frames of Reference in Classical Continuum Theory. In: An Expedition to Continuum Theory. Solid Mechanics and Its Applications, vol 210. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7799-6_8
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