Analytical Solutions in the Darboux Problem and the Bortz Equation and the Approach to Orientation Algorithms Based on Them

Статья подготовлена сотрудниками: д.т.н. Молоденков А.В.. к. ф.-м.н., доцент Сапунков Я.Г..
на базе: Лаборатория механики, навигации и управления движением.


Анотация

We consider the problem of determining the angular position of a rigid body in space from its known angular velocity and initial position (the Darboux problem) in the quaternion setting. Based on the exact solution of the Bortz approximate differential equation with respect to the orientation vector of the rigid body, we analytically solve the problem to determine the quaternion of the orientation of the rigid body for each arbitrary angular velocity and small rotation angle of the rigid body. Based on this solution, we propose an approach to design a new algorithm to compute the orientation of moving objects by means of strapdown inertial navigation systems.

Ключевые слова: analytical solution, orientation, arbitrary angular velocity, rigidanalytical solution, orientation, arbitrary angular velocity, rigid body, strapdown INS, qua- ternion, algorithm body, strapdown INS, qua- ternion, algorithm

DOI 10.3103/S002565442007016X

Ссылка на статью

Цитировать эту статью:

Molodenkov, A.V., Sapunkov, Y.G., Molodenkova, T.V. et al. Analytical Solutions in the Darboux Problem and the Bortz Equation and the Approach to Orientation Algorithms Based on Them. Mech. Solids 55, 1013–1020 (2020). https://doi.org/10.3103/S002565442007016X

О журнале Mechanics of Solids