Electromagnetic coil launchers offer the potential for extremely high efficiency, flexible, noncontacting, hypervelocity electromagnetic accelerators. Unfortunately, their implementation and development has been severely limited by the lack of compact power supplies capable of providing the required high energy and high powers. Integrating novel magnetic flux compression features into multistage rotating machines provides the flexible means for generating tailored, high-energy, high-power electromagnetic pulses required to efficiently drive these promising coil launchers. This paper presents advanced concepts of high energy power supplies for coil launchers. These concepts are designed to produce high inductive compression ratios and large current and magnetic field multiplication ratios in the range of megamperes of current and gigawatts of active power. As a consequence of the flexibility of multiwinding rotating generators, such designs provide an extensive range of output pulse shaping in single or multiple pulses, enabling optimum operation of the coil launcher. The interaction of different stationary and rotating electrical windings in strong magnetic fields with feedback generated amplification and nonuniform compensation of the armature reaction is the key to providing a large and flexible spectrum of tailored output pulses, eliminating the need for switching and other large external electromagnetic pulse forming components. Dynamic interactions between the internal impedance of these generators, and the induced electromotive forces in various windings, as well as the role of the external passive circuit components introduced in the launcher circuit, such as capacitors and inductors, are discussed and numerically evaluated. Finally, a new adaptive finite element method numerical code is described. This code takes into account the relative motion and is designed to evaluate machines incorporating flux compression.