MAXWELL’S REPRESENTATION OF THE SATELLITE APPROXIMATION POTENTIAL. ON ONE METHOD FOR DETERMINING THE MAIN AXES OF INERTIA OF A SOLID BODY USING THE PARAMETERS OF ITS SECOND-ORDER MULTIPOLE

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Abstract

Maxwell’s approach to the representation of homogeneous harmonic functions in the form of a superposition of derivatives in directions, developed by him within the framework of the study of problems of electrostatics, is applied to the representation of the potential of satellite approximation. The specified representation is determined by two unitary vectors located in a plane orthogonal to the intermediate axis of inertia of the body. In this case, the axis of inertia of the body corresponding to its smallest moment of inertia is the bisector of the angle formed by these vectors. The geometric meaning of the vectors is established: they are orthogonal to the circular sections of the body inertia ellipsoid constructed for the center of mass of the body. The above makes it possible to propose an approach to finding the main axes of inertia of a body based on Maxwell’s representation of its satellite approximation potential.

About the authors

E. A. Nikonova

FRC CSC RAS

Email: nikonova.ekaterina.a@gmail.com
Moscow

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