A model of charged energetic particle motion in a dipole field (in the range of rigidities from applicability of the adiabatic approximation up to the threshold of cosmic ray cut-off) is considered. The concept of the particle guiding centre trajectory is refined. TTie characteristics of this trajectory at the geomagnetic equator induce changes in a parameter which is the analogue of the pitch angle of a particle are studied. It is shown that when the adiabatic particle motion is violated due to the large rigidity of the particle, the particle conserves the analogue of the magnetic moment during motion from the equator to the mirror point and back. Violation of the magnetic moment (changes of an analogue of the particles’ pitch angle) occurs when the particle intersects the equatorial plane. The current model is used for the analysis of motion of particles with large rigidity. It is applied to study phenomena in the magnetosphere such as penetration of incompletely ionised nuclei into the magnetosphere and their stripping in the residual atmosphere. For incompletely ionised nuclei penetrating into the magnetosphere, conditions of particle motion and their penetration into the atmosphere for different stages of stripping are considered. A region of stable motion for repeated stripping of ions was found. The lifetimes of these particles is estimated.