Chebyshev output method for space motion state of rigid body

Abstract

The invention discloses a Chebyshev output method for the space motion state of a rigid body. The method comprises the steps of: defining a ternary number so that three speed components of the set of axes of the body and the ternary number form a system of linear differential equations; and performing approximation description on rolling, pitching and yawing angular speeds p, q and r by using Shifted Chebyshev orthogonal polynomials, wherein the state transfer matrix of the system can be solved in the manner of any order holder, thus obtaining the expression of the discrete state equation of the motion of the rigid body; and the problem of singularity of the attitude equation is avoided; therefore, the main motion state of the rigid body is obtained. The Chebyshev output method is characterized in that the ternary number is introduced so that the state transfer matrix is in the form of portioned upper triangles and thereby can be solved through deflation; therefore, the complexity of calculation is greatly simplified; and the Chebyshev output method is convenient for 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 of the large output error of the existing rigid body motion model, the present invention provides a Chebyshev 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 using Shifted Chebyshev (changing Chebyshev) orthogonal polynomials to approximate the roll, pitch, yaw angular velocity p, q, r, and can solve the state transition of the system in the way of any order holder matrix, and then obtain the expression of the discrete state equation of the rigid body motion, avoiding the singularity problem of the attitude equation, and thus obtaining the main motion state of the rigid body

Images