 Electric-dominated crossed-field orbit

Uniform perpendicular fields with $E^2>c^2{B}^2$ admit a subluminal Lorentz boost along $\mathbf{E}\times \mathbf{B}$ that eliminates the magnetic field. The transformed motion has constant transverse momentum and hyperbolic acceleration in the electric direction. An initially stationary laboratory particle generally has nonzero transverse velocity in this adapted frame; dropping it gives the wrong laboratory trajectory.