Fourier outputting method for spatial movement state of rigid body

Abstract

The invention discloses a Fourier outputting method for the spatial movement state of a rigid body. According to the invention, through defining tri-ary numbers, a linear differential equation set is established by three velocity components of body shafting and the tri-ary numbers; Fourier progression is utilized for approximation description of a rolling speed p, a pitching speed q and a yaw angle speed r; a state-transition matrix of a system can be solved according to the manner of an arbitrary-order holder so as to further obtain an expression of a discrete state equation of the motion ofthe rigid body; the singular problem of an attitude equation is avoided, and therefore, main motion state of the rigid body is obtained. In the invention, introduction of the tri-ary numbers enables the state-transition matrix to be in a partitioned upper triangular form, and the state-transition matrix can be solved in reduced order; therefore, the method substantially simplifies computational complexity and is convenient for utilization in works.

Description

technical field [0001] The invention relates to a space motion rigid body model, in particular to the problem of the output of a large maneuvering flight state of an aircraft. Background technique [0002] The differential equation of rigid body motion of the body shaft system is the basic equation describing the space motion of aircraft, torpedo, and spacecraft. Usually, in applications such as data processing, the state variables of the body axis system mainly include three velocity components, three Euler angles, and the X of the ground coordinate system. E , Y E ,Z E etc., due to Z E is defined as the vertical ground pointing towards the center of the earth, so Z E The actual negative flight altitude; X E , Y E Usually mainly rely on GPS, GNSS, Beidou, etc. to give directly; the Euler angle represents the attitude of the rigid body in space, and the differential equation describing the attitude of the rigid body is the core. Usually, the three Euler angles are pitc...

AI Technical Summary

Problems solved by technology

[0004] In order to overcome the problem of the large output error of the existing rigid body motion model, the present invention provides a Fourier output method of the rigid body space motion state. The method defines the ternary number so that the three velocity components of the body shaft system and the ternary number constitute Linear differential equations, and use Fourier series to approximate the roll, pitch, and yaw angular velocities p, q, r. The state transition matrix of the system can be solved according to any order holder, and then the rigid body motion can be obtained. The expression of the discrete state equation avoids the singularity problem of the attitude equation, and thus obtains the main motion state of the rigid body

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