Interpretation of the Equations of Motion in the Theory of Inertial Navigation

Abstract

The article presents the methodological and technological aspects of the theoretical analysis of the first group of motion equations (I. Newton’s dynamic equations), which are the core of the inertial navigation theory and systems. Conceptually, the notion of "analysis" is replaced by another methodological concept "interpretation" which "carries something significantly more important—the understanding that is necessary for producing new ideas" (Academician N. N. Moiseev). The purpose of the work is to verify and develop existing model concepts of motion based on their strict compliance with the axiomatics of Newtonian theory. By referring to the well-known matrix analysis procedure of symmetrization and alternation of a square matrix an expansion of the operator (3Ѕ3 dimension) of the total derivative of the differential motion equation is performed. The efficiency and relevance of the procedure is illustrated by an example of a partial solution of a two-point boundary value problem. The relevance of the decomposition of real square matrices of other dimensions for estimating their characteristic numbers is noted. The forms of the motion equations in various coordinate systems are presented. The general incorrectness of the Newtonian theory interpretation in a model of space built on a system of geodetic coordinates is shown due to the absence of attribute of the corresponding motion equations. At the same time, covariance takes place in a special identified case of motion.