The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of trea
ting Foucault and Bravais pendula as trajectories of the very same system of equations, each of them with particular initial conditions. We compare with the common two--dimensional approximations in textbooks. A previously unnoticed pattern in the three--dimensional Foucault pendulum attractor is presented.
In this work we use the Schwinger-Dyson equations to study the possibility that an enhanced gravitational attraction triggers the formation of a right handed neutrino condensate, inducing dynamical symmetry breaking and generating a Majorana mass for
the right handed neutrino at a scale appropriate for the see-saw mechanism. The composite field formed by the condensate phase could drive an early epoch of inflation. We find that to the lowest order, the theory does not allow dynamical symmetry breaking. Nevertheless, thanks to the large number of matter fields in the model, the suppression by additional powers in G of higher order terms can be compensated, boosting them up to their lowest order counterparts. This way chiral symmetry can be broken dynamically and the infrared mass generated turns out to be in the expected range for a successful see-saw scenario.
We show that the scalar field that drives inflation can have a dynamical origin, being a strongly coupled right handed neutrino condensate. The resulting model is phenomenologically tightly constrained, and can be experimentally (dis)probed in the ne
ar future. The mass of the right handed neutrino obtained this way (a crucial ingredient to obtain the right light neutrino spectrum within the see-saw mechanism in a complete three generation framework) is related to that of the inflaton and both completely determine the inflation features that can be tested by current and planned experiments.
