Legendre output method for space motion space of rigid body

Abstract

The invention discloses a Legendre output method for a space motion space of a rigid body. According to the method, three velocity components and triples of a machine body axis system form a linear simultaneous differential equation by defining the triples; the rolling p, the pitching q and the yaw rate r are subjected to approximation approximation description by adopting a Legendre orthogonal polynomial of a fluctuation zone; and a state transition matrix of the system is solved according to a mode of any-order holder, and thus an expression of a motion discrete-state equation of the rigid body is obtained, the singularity of an attitude equation is avoided and further main motion state of the rigid body is obtained. According to the Legendre output method disclosed by the invention, the triples are introduced, so that the state transition matrix is in a blocked upper triangular form and can be solved in an order reducing manner and the computation complexity is greatly simplified; and the Legendre output method is convenient for engineering to 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...

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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 Legendre 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 the Legendre orthogonal polynomials in the variable interval to approximate the roll, pitch, and yaw angular velocities p, q, and r, and can solve the state transition matrix of the system in the way of any order holder. Then the expression of the discrete state equation of the rigid body motion is obtained, which avoids the singularity problem of the attitude equation, and thus obtains the main motion state of the rigid body

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