Classical Mechanics (Kibble & Berkshire) · Problem 11.1

Lagrange's equations and conservation principles — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · non-standard-angular-momentum-principle

Problem

Non-standard angular momentum principle If AA is a generally moving point of space and LA\boldsymbol{L}_A is the angular momentum of a system S\mathcal{S} about AA in its motion relative to AA, show that the angular momentum principle for S\mathcal{S} about AA takes the non-standard form dLAdt=KA−M(R−a)×d2adt2.\frac{d\boldsymbol{L}_A}{dt} = \boldsymbol{K}_A - M(\boldsymbol{R} - \boldsymbol{a})\times\frac{d^2\boldsymbol{a}}{dt^2}. [Begin by expanding the expression for LA\boldsymbol{L}_A.] When does this formula reduce to the standard form? [This non-standard version of the angular momentum principle is rarely needed. However, see Problem 11.9.]

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