The three-dimensional nonlinear dynamics of atomic clouds in a magneto-optical trap is analyzed in terms of a self-consistent fluid formulation using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple-scattering effects are both relevant, in addition to damping. For closure, an adiabatic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriated spatial dependencies of the scalar potential and potential

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... d velocity field, a set of ordinary differential equations is derived. The linear stability analysis and the prominent features of the associated normal modes are characterized. Unlike previous treatments found in the literature, the current analysis applies to non-spherically symmetric trapped atomic gases. In addition, the use of a variational approach for a dissipative system is a further distinctive feature of the work. The paper is restricted to potential flows. topics: trapped atoms, time-dependent variational method, magneto-optical trap, normal modes