Perturbation multi-symplectic numerical solution containing disturbance system based on Hamiltonian theory

By using a perturbation-based multisymplectic numerical solution based on Hamiltonian theory, the problem of maintaining the system structure of nonlinear systems with perturbations in long-term simulations is solved, achieving high-precision dynamic response prediction and engineering applicability, which is suitable for aircraft design.

CN121525328APending Publication Date: 2026-02-13BEIHANG UNIV
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Patent Information

Application Number
CN202511779275.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-11-28
Publication Date
2026-02-13

AI Technical Summary

Technical Problem

Existing technologies struggle to efficiently and accurately solve the dynamic response of perturbation-containing nonlinear systems, especially in long-term simulations where maintaining the system's intrinsic physical structure and avoiding the accumulation of numerical errors are crucial issues.

Method used

A perturbation-based multisymplectic numerical solution method based on Hamiltonian theory is adopted. By constructing a multisymplectic Hamiltonian system, the Preissmann Box multisymplectic difference scheme is used for numerical solution. The symplectic structure characteristics of the system are preserved, and the system is decomposed into a series of linear multisymplectic Hamiltonian equations to obtain a high-precision dynamic response.

Benefits of technology

It achieves high-precision long-term dynamic behavior prediction, reduces computational costs, improves the structural preservation and engineering applicability of numerical solutions, and is suitable for aircraft design and analysis.

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Abstract

The invention discloses a Hamiltonian theory-based perturbation multi-symplectic numerical solution containing a disturbance system, and belongs to the technical field of numerical calculation of a nonlinear dynamic system. The method comprises the following steps: firstly, establishing a mathematical model containing a disturbance mechanical structure, converting the mathematical model into a Dosin Hamiltonian system, introducing small parameters to unfold the system into a power series form, and decomposing an original system into a series of linear Dosin Hamiltonian equations through a perturbation theory; and carrying out numerical solution on the perturbation equation of each order by adopting a Preissmann Box Dosin difference format, and finally synthesizing a dynamic response solution of the system. According to the method, the influence of small disturbance on long-term dynamic behaviors is effectively captured while the sympathetic structure of the system is maintained, the method has the characteristics of high precision and strong structure maintenance, the method is suitable for dynamic response analysis of disturbance-containing mechanical systems and generalized nonlinear systems, and an efficient and reliable numerical tool is provided for design and optimization of engineering structures such as aircrafts.
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