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Chapter 10: Q7P (page 513)
Write in terms ofas inand:
(a)(b)
The terms of part and areand
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Generalize Problem 3 to see that the direct product of any two isotropic tensors (or a direct product contracted) is an isotropic tensor. For example show thatis an isotropic tensor (what is its rank?) andis an isotropic tensor (what is its rank?).
Point masses 1 at (1, 1, -2) and 2 at (1, 1, 1).
The square matrix in equation is called the Jacobian matrix J; the determinant of this matrix is the Jacobian which we used in Chapter 5 , Section 4 to find volume elements in multiple integrals. (Note that as in Chapter 3, J represents a matrix; J in italics is its determinant.) For the transformation to spherical coordinates in localid="1659266126385" and show that . Recall that the spherical coordinate volume element is . Hint: Find and note that
For Example 1, write out the components of U,V, and in the original right-handed coordinate system and in the left-handed coordinate system S' with the axis reflected. Show that each component ofinS'has the 鈥渨rong鈥� sign to obey the vector transformation laws.
In spherical coordinates.
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