Emmett output method for rigid body space motion state

Abstract

The invention discloses an Emmett output method for rigid body space motion state, wherein the method comprises the following steps of: defining ternary number, so that three speed components of a machine body shaft system and the ternary number form simultaneous differential equations; using an Emmett orthogonal polynomial to carry out approximation description to rolling, pitching and yaw ratesp, q and r; solving a state transition matrix of the system according to the manner of an any-order retainer to acquire an expression of a movement discrete state equation of the rigid body, avoidingan attitude equation singularity problem to acquire the main motion state of the rigid body. The method is introduced with the ternary number, so that the state transition matrix is in the form of a blocked upper triangle, can be solved in an order-reducing manner, thus the calculating complexity is greatly simplified for the convenience of engineering use.

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 that the output error of the existing rigid body motion model is large, the present invention provides an Emmett 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 Hermitian orthogonal polynomials to approximate the roll, pitch, and yaw angular velocities p, q, and r, the state transition matrix of the system can be solved according to any order holder, 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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