RESUMEN
In planar nano-magnetic devices magnetization direction is kept close to a given plane by the large easy-plane magnetic anisotropy, for example by the shape anisotropy in a thin film. In this case magnetization shows effectively in-plane dynamics with only one angle required for its description. Moreover, the motion can become overdamped even for small values of Gilbert damping. We derive the equations of effective in-plane dynamics in the presence of spin-transfer torques. The simplifications achieved in the overdamped regime allow to study systems with several dynamic magnetic pieces ("free layers"). A transition from a spin-transfer device with a static polarizer to a device with two equivalent magnets is observed. When the size difference between the magnets is less than critical, the device does not exhibit switching, but goes directly into the "windmill" precession state.