There is little doubt that the magnetization dynamics of ferromagnetic systems is governed by the Landau-Lifshitz-Gilbert equation or its generalization with various spin torques. In contrast, there are several sets of dynamic equations for two-sublattice antiferromagnets (AFMs) in literature that have different forms of dissipative torques and no proper dynamic equations for multi-sublattice AFMs and ferrimagnets in general. Here we introduce the general Rayleigh dissipation functional into the Lagrange equation and derive the proper form of the dissipative torques in the phenomenological equations for the AFMs with multiple sublattices. A new type of dissipative torque arising from inter-sublattice drag effect is discovered that has important influences on magnon lifetime and domain wall motion. In particular, our theory unifies different dynamic equations of AFMs in literature.