Nuclear deformation and rotation can be described by collective, macroscopic models such as the liquid drop model, or by microscopic theories like the shell model, using one-body operators acting on single particle wavefunctions Algebraic mean field theory (AMFT) constructs coadjoint orbits in the dual space of a Lie algebra made up of one-body operators. The coadjoint orbits are made up of densities corresponding to the quantum mechanical expectations of the one-body operators on the single particle wavefunctions. It reduces an infinite-dimensional problem in the shell model to a problem on a finite-dimensional manifold involving simple matrix multiplication. The critical points of a realistic energy functional on the coadjoint orbit produce equilibrium solutions for a rotating ellipsoid In this paper, AMFT has been applied to the symplectic algebra sp(3,reals), which encompasses both the su(3) algebra of the shell model, and the gcm(3) algebra that is the dynamical symmetry algebra of Riemann ellipsoid theory