Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.

Simulation of a resonant inverter

Mostly developed since the Industrial Revolution, the automation of systems and equipment around us is responsible for a technological progress and economic growth without precedents, but also by a relentless energy dependence. Currently, fossil fuels still tend to come as the main energy source, even in developed countries, due to the ease in its extraction and the mastery of the technology needed for its use. However, the perception of its ending availability, as well as the environmental impact of this practice has led to a growing energy production originated from renewable sources. Easy maintenance, coupled with the fact that they are virtually inexhaustible, makes the solar and wind energy very promising solutions. In this context, this work proposes to facilitate energy production from these sources. To this end, in this work the power inverter is studied, which is an equipment responsible for converting DC power available by solar or wind power in traditional AC power. Then it is discussed and designed a new architecture which, in addition to achieve a high energy e - ciency, has also the ability to adapt to the type of conversion desired by the user, namely if he wants to sell electricity to the power grid, be independent of it or bet on a self consumption system. In order to achieve the promised energy e ciency, the projected inverter uses a resonant DC-DC converter, whose architecture signi cantly decreases the energy dissipated in the conversion, allowing a higher power density. The adaptability of the equipment is provided by an adaptive control algorithm, responsible for assessing its behavior on every iteration and making the necessary changes to achieve maximum stability throughout the process. To evaluate the functioning of the proposed architecture, a simulation is presented using the PLECS simulation software.