3-d Relative Time Derivatives

(Lecture: 30 minutes)

  • Recover modified second law
  • Coriolis and centrifugal acceleration

Lecture notes (alternate derivation)


This lecture generalizes the results in the 2-dimensional case to 3 dimensions. The comments made there apply even more so in this case – apart from the value in reviewing spherical basis vectors, students will have little interest in, effectively, repeating the same derivation in a slightly different context.

One route through these various issues is to briefly discuss the correction terms between “naive” and “true” time derivatives of the spherical basis vectors, point out that the form of the resulting expressions is the same as in the 2-dimensional case, so that the further derivation — and hence the final result — have the identical form in both cases.

Regardless of the approach chosen, the instructor should take care to adequately motivate the mathematial derivation.

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