Hartley output method of rigid body space motion states

Abstract

The invention discloses a Hartley output method of rigid body space motion states, which enables three velocity components and a ternary figure of a body axis to form linear simultaneous differential equations by defining the ternary figure, and adopts a Hartley function to conduct approximate approaching description of roll rate P, pitching rate Q and yaw rate R. Users can solve a state-transition matrix of a system in accordance with arbitrary order keeper modes, and then obtain expression of rigid motion discrete state equations, thereby avoiding gesture equation strange problems and obtaining main motion states of a rigid body. The Hartley output method enables the state-transition matrix to be a blocking upper triangular form by introducing the ternary figure, can reduce order to solve the state-transition matrix, greatly simplifies computational complexity and is convenient to use in construction.

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 large output error of the existing rigid body motion model, the present invention provides a Hartley 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 a linear differential Equations, and use the Hartley function to approximate the roll, pitch, and yaw angular velocities p, q, and r. The state transition matrix of the system can be solved in the way of any order holder, and then the expression of the discrete state equation of rigid body motion can be obtained. formula, which avoids the singular problem of the attitude equation, and thus obtains the main motion state of the rigid body

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