An effective energy of a central force system is constructed as E_eff = 1/2m(r˙)^2 + U_eff(r), where U_eff(r) = U(r) + L_0^2/2mr^2, and U(r) is the potential energy. For the conserved energy system, the total energy generally writes as E = T + U(r) = 1/2mv^2 + U(r), where T is the kinetic energy. Show that E_eff is indeed equivalent to the total energy of this system.
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