By Tadmor E.B, Miller R.E., Elliott R.S.

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**Extra resources for Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations**

**Example text**

51]. t Scalars, vectors and tensors 12 Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to bodies and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Relative, apparent, and common time is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year.

Using Eqn. 3 What is a tensor? 31 or in determinant form ⎡ c1 (a × b) · c = det ⎣a1 b1 c2 a2 b2 ⎤ c3 a3 ⎦ . 4 Change of basis We noted earlier that the choice of basis vectors ei is not unique. There are, in fact, an infinite number of equivalent basis sets. Consider two orthonormal bases eα and ei as shown in Fig. 2. For the sake of clarity, we adopt Sokolnikoff notation where (with a wink to ancient history) Greek indices refer to the “original” basis and Roman indices refer to the “new” basis.

It is not surprising, therefore, that Newton considered his discovery of these concepts to be his most important achievement [Gre04]. Frame of reference In practice, Newton recognized that it is not possible to work directly with absolute space and time since they cannot be detected, and so he introduced the concepts of relative space and relative time [New62]: 4 5 Recall that the word planet comes from the Greek “planetai” meaning “wanderers,” because the planets appear to move relative to the fixed backdrop of the stars.