Laguerre output method for rigid body space motion state

Abstract

The present invention discloses a Laguerre output method for a rigid body space motion state. According to the method, three velocity components of a machine shaft system and a three-ary number form linear differential equations by defining the three-ary number; a Laguerre orthogonal polynomial is adopted to proximately and closely depict a rolling angle p, a pitching angle q, and a yawing angular velocity r; a state transition matrix of the system can be solved according to a manner of an arbitrary order keeper so as to acquire an expression of a rigid body motion discrete state equation, such that the singularity problem of the attitude equation is avoided so as to acquire the main motion state of the rigid body. According to the present invention, the three-ary number is introduced, such that the state transition matrix is the block upper triangular manner, and can be solved by reducing the order so as to substantially simplify the calculation complexity, and be easily used by the engineering.

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 Laguerre output method for the state of motion of the rigid body in space. 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 using Laguerre orthogonal polynomials 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 retainer, and then the rigid body can be obtained The expression of the discrete state equation of motion avoids the singularity problem of the attitude equation, thereby obtaining the main motion state of the rigid body

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