One pendulum to run them all

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

The crystal morphology and growth rates of triclinic N-docosane crystallising from N-dodecane solutions

A detailed analysis of the crystal morphology of triclinic n-docosane (C22H46) is presented together with a preliminary assessment of the supersaturation-dependence of the growth rates for the predicted (hkl) faces. A methodology to index the experimentally observed crystal faces, based on a combined BFDH and zone axis methodology is defined. Analysis using this methodology yields the morphological indexation of n-docosane to be (001), (112), (102), (010), and (1 - 33) or (130) based on the expected triclinic crystal structure. Crystals of n-docosane growing from supersaturated n-dodecane (C12 H26) solutions, as studied using in-situ optical microscopy, at three different supersaturation (σ) levels 0.01, 0.02 and 0.05, reveal that the crystal morphology changes with increasing in supersaturation, evolving from a habit consistent with a triclinic crystal system to a habit that is perhaps more representative of an orthorhombic structure. Growth rates determined for the (112) and (102) faces as well as for those less dominant faces range between 0.51 and 9.85 mm/s, in good agreement with previously reported data for other organic molecules including n-alkanes