THEORY OF MOTION OF A THIN METALLIC CYLINDER CARRYING A HIGH CURRENT.
Geophysical research papers,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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A simple-looking nonlinear differential equation of motion is found for a thin metallic cylinder carrying a high sinusoidal current. It shows the radius to be its initial value multiplied by a function depending only on two quantities, k and omega t, where t is the time and k is a parameter which depends on the initial radius and mass per unit length of the cylinder and on the amplitude and angular frequency omega of the current. The solutions obtained show the radius to decrease, gradually at first, then more and more rapidly until the cylinder collapses. The time for the cylinder to collapse depends only on k and is equal to the current rise time for a unique valud k sub o of k. A simple expression found for the radius is exact for times near zero, becomes increasingly lower than the correct radius, and finally goes to zero at a time 1 or 2 less than the correct collapse time for k near k sub o. An accurate method, also good for other current rise forms, is derived and applied for two values of k to give the radius as a function of time. The results lead to the collapse time equal to 12 omega TT - 3.79k - k sub o for k near k sub o 0.2596 plus or minus 0.0008. Author
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