The equation of motion for a charged particle moving in the n-dimensional c
onstant magnetic field is obtained for any linear gauge and any metric tens
or by generalization of Johnson and Lipmann's approach. It allows to consid
er the magnetic orbits in the n-dimensional space. It is shown that the mov
ement of a particle can always be decomposed into a number of two-dimension
al cyclotronic motions and a free particle part.