哈尔滨工程大学学报2018，Vol.39Issue(1)：33-39,7.DOI:10.11990/jheu.201611054
Lagrange方程应用于流体动力学
Application of Lagrange equation in fluid mechanics
摘要
Abstract
The application of the Lagrange equation to fluid dynamics is difficult in theoretical research.In accord-ance with basic theory research on the calculus of variations, the concept of the variational derivative and algorithm are applied.The Lagrange equation is applied to ideal fluid dynamics gradually by studying the property of deriva-tion from the Lagrange equation.The Lagrange-Hamilton system, which is the Lagrange equation of a non-conserva-tive system, is a quasi-stationary condition of Hamilton-type quasi-variational principle of a non-conservative sys-tem.The Lagrange equations for incompressible viscous fluid dynamics are derived from the Hamiltonian quasi-vari-ational principle of the incompressible viscous fluid dynamics successfully.The governing equations of incompressi-ble viscous fluid dynamics are deduced from the Lagrange equation of incompressible viscous fluid dynamics.Final-ly, application of the Lagrange equation to the questions of compressible viscous fluid dynamics is discussed.This paper comprehensively describes how to apply the Lagrange equation to fluid dynamics.关键词
Lagrange方程/Lagrange-Hamilton体系/变导/理想流体动力学/黏性流体动力学Key words
Lagrange equation/Lagrange-Hamilton system/variational derivative/ideal fluid dynamics/viscous fluid dynamics分类
数理科学引用本文复制引用
梁立孚,周平..Lagrange方程应用于流体动力学[J].哈尔滨工程大学学报,2018,39(1):33-39,7.基金项目
国家自然科学基金项目(10272034). （10272034）
