Arbitrary-step orthogonal series output method of space motion state of rigid body

Abstract

The invention discloses an arbitrary-step orthogonal series output method of the space motion state of a rigid body. In the method, a ternary number is defined so that the three velocity components of a body axis system and the ternary number form linear simultaneous differential equations; the rolling angular velocity p, pitching angular velocity q and yawing angular velocity r are subjected to similar approximation description by use of an arbitrary-step orthogonal polynomial; and a state transition matrix of the system can be solved according to the mode of an arbitrary-order holder so as to obtain an expression of a motion discrete state equation of the rigid body, avoid the problem of singularity of an attitude equation and obtain the major motion state of the rigid body; and in the invention, the state transition matrix becomes a block upper triangular matrix by introducing the ternary number, and the state transition matrix can be solved by reducing order, thereby greatly reducing the computational complexity and facilitating the engineering application.

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 modeling method for the output model of an arbitrary step-length orthogonal series of the rigid body motion state in space. Velocity components and ternary numbers constitute a linear differential equation system, and use arbitrary step size orthogonal polynomials to approximate the roll, pitch, and yaw angular velocities p, q, and r, and can solve the system in the way of any order retainer The state transition matrix, and then obtain the expression of the discrete state equation of the rigid body motion, avoiding the singularity problem of the attitude equation, thereby obtaining the main motion state of the rigid body

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