Wandering Among Newton Wonders
Donald Lynden-Bell
Abstract
In the electromagnetic fields t2 B = b(r/t), E = r x B/t trajectories of non-relativistic charged particles conserve (r-vt)2. The transformation r'=r/t t'=1/t maps such trajectories into orbits in the constant magnetic field all of which conserve kinetic energy. The transformation may also be used to transform any fields obeying Curl E = B/dt, div B = 0 into others and relates the particle trajectories in them.
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