Plumpton-Ferraro Oscillations of a Slowly Rotating Liquid Sphere

Summary In a dissipative system the decay of a dependent variable h (say) released in the form of a Dirac delta function usually occurs instantaneously, so that h is bounded for t > 0. This apparently releases infinite amounts of energy, since ½∫h2dx is initially unbounded. In a non-dissipative system such as a slowly rotating liquid sphere in a uniform magnetic field we infer that the infinite energy of an initial disturbance in the form of an oscillating Plumpton–Ferraro shell would render it able to oscillate ‘for ever’; but it would also gradually transmit energy to the nearpoloidal modes of oscillation and the other Plumpton–Ferraro shells. This problem is discussed by utilizing a model which permits simple Fourier analysis. The evolution of initial pulses of various spatial widths is discussed, and the results found to agree with physical inference. The model has been linearized, and this should be borne in mind when interpreting results as the delta function is of infinite amplitude.