Refinement of the Oblique Dipole Model in the Evolution of Rotary Motion of a Charged Body in the Geomagnetic Field

Abstract

When solving problems related to the induction of the Earth's magnetic field, the potential of which is expressed in the form of a series of spherical harmonic functions, it is necessary to use an approximate model of the geomagnetic field that satisfies the two conflicting requirements of simplicity and accuracy. As is noted in [3, p. 10], at the stage of design of satellites, especially at the stage of preliminary analysis of their dynamics, simple models of the geomagnetic field are usually employed. This offers additional possibilities for theoretical analysis of the problem. The averaged model and the model of a right dipole are just such simple models. The quadrupole model of the geomagnetic field developed in [4] is more accurate, but also more complex. The model of an oblique or skewed dipole is intermediate. The quadrupole model generalizes the simpler models mentioned above, and its analysis allows estimation of the accuracy of each model. It turns out that the oblique dipole model, which differs from the model of a right dipole by small correcting terms, does not take into account other correcting terms caused by the quadrupole part of the geomagnetic field, which are greater in magnitude. The evolution of the rotary motion of a charged rigid body in the geomagnetic field is considered, and the incorrectness of the oblique dipole model is demonstrated. The effect of the quadrupole component of the geomagnetic field on the body dynamics is revealed.