## An asymptotic approximation method for a system with rotating phases and its application to the motion of a charged particle in a magnetic field |

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accuracy adiabatic invariant angular variable application ASYMPTOTIC APPROXIMATION METHOD average motion Bogolyubov center of gravity change of variables changes very little charged particle coefficients component condition 1.1 cosmic electrodynamics CURVILINEAR COORDINATE D. N. Zubarev describes the motion drift velocity produced electric and magnetic equations 3.9 equations of motion expansion expresses field is sufficiently Fourier series guiding center harmonic immediately applied inhomogeneity Journal VII large and uniform Larmor circle Larmor frequency Larmor radius magnetic field changes magnetic field line MAGNETIC FIELD N. N. method of asymptotic non-uniform electric non-uniform field non-uniform magnetic field non-uniqueness numerical calculation obtain order of approximation paragraph parameter particle in non-uniform particle velocity perpendicular perturbation theory physical meaning possible to construct problem quantity rapidly rotating phase right hand sides shivering supplementary condition system of equations SYSTEM WITH ROTATING systematic motion takes the form terms of order Translated by BURTON TRANSLATOR'S unit vectors zeroth