We study the radiation generated by electric currents in (1) infinite cylinders with longitudinal flow, (2) infinite cylinders with solenoidal flow, and (3) infinite planes. In each case we work out four specific examples, for which the retarded fields can be calculated exactly, and we derive a "Larmor-like" formula for the power radiated, in the limit of infinitesimal cross-section. We then consider sinusoidal currents with finite cross-section, and discover that for certain special frequencies the external fields are zero and there is no radiation. We relate our results to the work of Goedecke and others, and conclude with some remarks on the radiation reaction in these configurations.

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We  examine the motion of an Atwood’s Machine in which one of the masses is allowed to swing in a plane. Computer studies reveal a rich variety of trajectories. The orbits are classified (bounded, periodic, singular, and terminating), and formulas for the critical mass ratios are developed. Perturbative techniques yield good approximations to the computer-generated trajectories. The model constitutes a simple example of a nonlinear dynamical system with two degrees of freedom.