Polynomial type output method for spatial motion state of rigid body

Abstract

The invention discloses a polynomial type output method for a spatial motion state of a rigid body. In the method, by defining a ternary number, three speed components of a machine body axis system and the ternary number constitute a linear simultaneous differential equation, polynomials are used for performing approximate description on roll rate p, pitch rate q and yaw rate r, a state-transition matrix of a system can be solved according to a random-order keeper manner so as to further obtain an expression of a motion discrete state equation of the rigid body, and thus, the problem of a singular gesture equation is avoided and the main motion state of the rigid body is obtained. In the invention, by introducing the ternary number to make the state-transition matrix be of a blocked upper triangular form, the state-transition matrix can be solved in a reduced order manner, the computation complexity is greatly simplified, and engineering purposes are facilitated.

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. Since ZE is defined as the vertical ground pointing to the center of the earth, 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 pitch, roll and ...

AI Technical Summary

Problems solved by technology

[0004] In order to overcome the problem of large output error of the existing rigid body motion model, the present invention provides a polynomial output method of the rigid body space motion state. The method defines a ternary number so that the three velocity components of the body shaft system and the ternary number form a linear Differential equations, and use 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 the method of any order holder, and then the discrete state equation of rigid body motion can be obtained. The expression avoids the singular problem of the attitude equation, and thus obtains the main motion state of the rigid body

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