Classical Dynamics of Particles and Systems · Problem 8-13

Dynamics of a System of Particles — Marion & Thornton

Physics — Mechanics · central-force-precessing-ellipse-inverse-cube

Problem

Discuss the motion of a particle in a central inverse-square-law force field for a superimposed force whose magnitude is inversely proportional to the cube of the distance from the particle to the force center; that is, F(r)=−kr2−λr3k, λ>0F(r) = -\frac{k}{r^2} - \frac{\lambda}{r^3} \quad k,\, \lambda > 0 Show that the motion is described by a precessing ellipse. Consider the cases λ<l2/μ\lambda < l^2/\mu, λ=l2/μ\lambda = l^2/\mu, and λ>l2/μ\lambda > l^2/\mu.

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