In a static magnetic field, some well-known guiding center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the mag¬netic moment series. The differential equation for guiding center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition.
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