System of differential equations of aircraft spatial motion dynamics with arbitrary tensor of inertia and center of gravity position

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Derivation of analytic expressions making up the basis of a mathematical model of aircraft flight dynamics for the differential equations describing the change in the rate of roll, yaw and pitch, as well as flight velocity components in projections on the body-fixed coordinate axes is presented. The origin of the coordinate system does not in general coincide with the center of mass of the plane, and the axes are not the same as its main central axes of inertia. The differential equations for angular and linear velocities are reduced to the form convenient for the use of numerical methods and computer systems and make it possible  to get consistent results of simulating the dynamics of aircraft spatial motion with an arbitrary tensor of inertia and center of gravity position.

About the authors

D. V. Vereshchikov

Military Educational and Scientific Center of the Air Force Academy named after Professor N.E. Zhukovsky and Yu.A. Gagarin

Author for correspondence.

Candidate of Science (Engineering), Associate Professor, Head of Department

Russian Federation


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