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Chapter 10: Q8P (page 502)
Write the equations in (2.16) and so in (2.17) solved for the unprimed components in terms of the primed components.
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Interpret the elements of the matrices in Chapter 3, Problems 11.18 to11.21, as components of stress tensors. In each case diagonalize the matrix and so find the principal axes of the stress (along which the stress is pure tension or compression). Describe the stress relative to these axes. (See Example 1.)
Observe that a simpler way to find the velocity in (8.10)is to divide the vectordsin (8.6)by. Complete the problem to find the acceleration in cylindrical coordinates.
What are the physical components of the gradient in polar coordinates? [See (9.1)].The partial derivatives in (10.5) are the covariant components of. What relationdo you deduce between physical and covariant components? Answer the samequestions for spherical coordinates, and for an orthogonal coordinate system withscale factors.
P Derive the expression (9.11)for curl V in the following way. Show that and . Write V in the form and use vector identities from Chapter 6 to complete the derivation.
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