A particle with mass m, position r' and momentum p has angular momentum M = 7 x p. (a) Evaluate {x,, M}, {Pj, Mk}, {M, Mk} and {M, M}. (b) Consider a particle of mass m moving in a central potential V(r) = -mK/r. Recall the Runge- Lenz vector A = px M - mKf. Show that 2H {M, Aj} = ijk Ak, {A, Aj} = m Prove using Poisson brackets that A is conserved. (Also note that A, M and H form a closed algebra under the Poisson bracket.) -tijk Mk.