This is related to Goldstein Exercise 3-28. It is not really a homework problem anymore because I have solved them. But there's something bugging me so I shall post here instead of under homework problem. The Exercise reads:(adsbygoogle = window.adsbygoogle || []).push({});

A magnetic monopole has magnetic monopoleB= br/r^3 where b is a constant. Suppose a particle of mass m moves in the field of a magnetic monopole and a central force field derived from the potential V(r)=-k/r.

(a) Show that there is a conserved vectorD=L- (qb/c)r/r.

(b) Show that for some f(r) there is a conserved vector analogous to the Laplace-Runge-Lenz vector in whichDplays the same role asLin the pure Kepler force problem.

If you look at http://arxiv.org/abs/nlin/0504018. There is a comment right before Eq.9 where they remarked that "there is no analogue of the integral A (the LRL vector) in the Poincare and Appell problems".

Poincare problem is the pure magnetic charge case without central force (k=0) while Appell problem seems to be the one in Goldstein's exercise [of a particle moving in the field of a Newtonian center and in the field of a magnetic monopole, assuming that the center and the monopole coincide]. So my question is, did I misunderstood this somehow and Goldstein exercise is not really the Appell problem?

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# Laplace-Runge-Lenz Vector for Magnetic Monopole

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