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Chapter 10: Q5P (page 520)
Show by the quotient rule (Section 3 ) that in is a -rank tensor.
The statement has been proven.
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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.
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.
Using cylindrical coordinates write the Lagrange equations for the motion of a particle acted on by a force, where V is the potential energy. Divide each Lagrange equation by the corresponding scale factor so that the components of F (that is, of
) appear in the equations. Thus write the equations as the component equations of
, and so find the components of the acceleration a. Compare the results with Problem
.
Write equations (2,11), (2,12),(2,13),(2,14),(2,16),(2,17),(2,18) using summation convention.
Bipolar.
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