5. A particle of mass m moves in a central force field with potential V(r). The Lagrangian in terms spherical coordinates (r, 0,4) is L= m(r²+r²²+r²sin2062) (a) Find the momenta (pr. Pe. Po) conjugate to (r, 0, 0). (b) Find the Hamiltonian H(r,0,.Pr. Po. Po). (c) Write down the explicit Hamilton's equations of motion and identify any constant of motion. (d) Calculate the following Poisson brackets: (i) [mr, mé] (ii) [mr, pr]. (iii) [mr, H]