Introduction to Classical Mechanics · Problem 7.3

Angular momentum, Part I (Constant L) — Morin

Physics — Mechanics · central-forces-effective-potential

Problem

Maximum

L

*** A particle moves in a potential,

V(r) = -V_0 e^{-\lambda^2 r^2}

. ((a)) Given

L

, find the radius of the stable circular orbit. An implicit equation is fine. ((b)) It turns out that if

L

is too large, then no circular orbit exists. What is the largest value of

L

for which a circular orbit does in fact exist? If

r_0

is the radius of the circle in this cutoff case, what is the value of

V_{\rm eff}(r_0)