Ionospheric electron under non-uniform acceleration

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Vijay Manoj
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In 'Introduction to Mechanics' by Kleppner and Kolenkow...motion of ionospheric electron under non-uniform acceleration is x = (a0/w)t - (a0/w^2)sin wt...my question is when there is non-uniform acceleration, it makes sense to have sinusoidal part in the motion...but how come there is uniform motion (a0/w)t is also present ? does this two parts of motion have physical meaning behind it ? thanks in advance guys...
 
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See this page and the links in the references part!
Also read any text that calculates the trajectory of a charged particle in a non-uniform magnetic field.I'm not sure but maybe you can find such a text in the references part of the above page.