Chapter 10: Q9 P (page 517)
Short Answer
F and E are polar vectors.
Chapter 10: Q9 P (page 517)
F and E are polar vectors.
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Parabolic cylinder coordinates
Write the tensor transformation equations for to show that this is a (rank 6) tensor (nota pseudo tensor). Hint:Write (6.1) for eachand multiply them, being careful not to re-use a pair of summation indices.
Show that (3.9) follows from (3.8) . Hint: Give a proof by contradiction. Let be the parenthesis in ; you may find it useful to think of the components written as a matrix. You want to prove that all 9 components of are zero. Suppose it is claimed that is not zero. Since is an arbitrary vector, take it to be the vector
, and observe that is then not zero in contradiction to
.Similarly show that all components of are zero as
claims.
Find the inertia tensor about the origin for a mass of uniform density =1, inside the part of the unit sphere where and find the principal moments of inertia and the principal axes. Note that this is similar to Example 5 but the mass is both above and below the plane. Warning hint: This time don’t make the assumptions about symmetry that we did in Example 5.
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