Inertial Navigation in Space Using the Regular Quaternion Equations of Astrodynamics

• Published in: Mechanics of solids Vol. 54; no. 2; pp. 157 - 168
• Main Author: Chelnokov, Yu. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.03.2019; Springer Nature B.V
• Subjects: Algorithms; Astrodynamics; Astronavigation; Celestial mechanics; Classical Mechanics; Earth gravitation; Gravitational fields; Inertial navigation; Mathematical analysis; Navigation systems; Physics; Physics and Astronomy; Quaternions; Stabilized platforms; Strapdown inertial navigation; Two body problem; inertial navigation; spacecraft; Kustaanheimo-Stiefel variables; astrodynamics; regular quaternion equations of inertial navigation; platform and strapdown inertial navigation systems
• ISSN: 0025-6544; 1934-7936
• DOI: 10.3103/S0025654419030063

Quaternion equations are proposed for the ideal operation of spatial inertial navigation systems with an azimuthally stabilized platform and a gyrostabilized platform that keeps its orientation invariant in inertial space, quaternion equations for the ideal operation of strapdown inertial navigation systems in the regular four-dimensional Kustaanheimo-Stiefel variables with consideration of zonal, tesseral, and sectorial harmonics of the Earth's gravitational field. The equations are dynamically similar to the regular equations of perturbed spatial two-body problem in the Kustaanheimo-Stiefel variables, which enables to use the results obtained in regular celestial mechanics and astrodynamics theory in inertial astronavigation. The development of operational algorithms for these navigation systems using these equations is considered.