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Barenboim, G., & Oteo, J. A. (2013). One pendulum to run them all. Eur. J. Phys., 34(4), 1049–1065.
Abstract: The analytical solution for 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 treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.
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Blanes, S., Casas, F., Oteo, J. A., & Ros, J. (2010). A pedagogical approach to the Magnus expansion. Eur. J. Phys., 31(4), 907–918.
Abstract: Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.
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