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Application of Lagrange＇s equation to rigid-elastic coupling dynamics

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Science China(Technological Sciences) 2017年第8期60卷 1263-1277页

作者： FENG XiaoJiu liang lifu SONG HaiYan School of Environmental and Safety Engineering Changzhou University Changzhou 213164 China College of Aerospace and Civil Engineering Harbin Engineering University Harbin 150001 China

A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum *** paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear *** accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's *** addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.

关键词： nonlinear rigid-elastic coupling dynamics Lagrange's equation variational derivative

Non-linear and non-conservative quasi-variational principle of flexible body dynamics and application in spacecraft dynamics

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Science China(Physics,Mechanics & Astronomy) 2013年第11期56卷 2192-2199页

作者： liang lifu SONG HaiYan School of Civil Engineering Harbin Engineering University

The law of conservation of energy is one of the most fundamental laws of *** to the law of the conservation of energy,the non-linear and non-conservative quasi-variational principle of flexible body dynamics is *** physical meaning of the quasi-stationary value conditions has been explained in non-linear and non-conservative flexible body *** the case study,the application in spacecraft dynamics is researched.

关键词： non-linear non-conservative variational principle spacecraft dynamics flexible body

ON THE RELATIONSHIP BETWEEN THE VACCO MODEL AND CHETAEV MODEL

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Acta Mechanica Solida Sinica 1994年第3期7卷 274-283页

作者： liang, lifu liang, Zhongwei Harbin Shipbuilding Engineering Inst Harbin China

In this paper, the geometric property and the mechanical property of non-holonomic constraints are studied. Vacco equation is obtained by using the classical Hamilton principle. On the basis of Vacco equation, Chetaev condition is obtained by using mechanics principle of determining the ideal constraint. It is pointed out that the Vacco model is compatible with Chetaev model, so these two kinds of models are unified.

关键词： Constraint theory Geometry Mechanical properties Mechanics Velocity

Lagrangian theoretical framework of dynamics of nonholonomic systems

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Science China(Physics,Mechanics & Astronomy) 2007年第6期50卷 766-778页

作者： liang lifu HU HaiChang CHEN DeMin College of Civil Engineering Harbin Engineering UniversityHarbin 150001China Institute of Spacecraft System Engineering Chinese Academy of Space TechnologyBeijing 100086China College of Vehicle Engineering Beijing Institute of TechnologyBeijing 100081China

By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.

关键词： generalized variational principle nonholonomic systems Chetaev’s model Vakonomic model the Lagrangian clas-sical relationship the Lagrangian theoretical framework

Unconventional Hamilton-type variational principles for analytical mechanics

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Science China(Physics,Mechanics & Astronomy) 2007年第2期50卷 152-162页

作者： LUO En liang lifu LI WeiHua Department of Applied Mechanics and Engineering Sun Yat-sen UniversityGuangzhou 510275China Department of Aerospace Engineering Harbin Engineering UniversityHarbin 150001China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.

关键词： analytical mechanics holonomic and nonholonomic systems unconventional Hamilton-type variational principle dual-complementarity initial-value problem restricted variation

Quasi-variational principles of single flexible body dynamics and their applications

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Science China(Physics,Mechanics & Astronomy) 2009年第5期52卷 775-787页

作者： liang lifu LIU ShiQuan ZHOU JianSheng School of Civil Engineering Harbin Engineering UniversityHarbin 150001China China Sanjiang Space Industry Group Corp Wuhan 430015China

The reasons for studying single flexible body dynamics are that on one hand,it is the basis of flexible multi-body *** the theory of the single flexible body dynamics has been deeply studied,the theory of flexible multi-body dynamics will be researched *** the other hand,it has its unique and important ***-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body mechanics and deformable body *** the interceptor as an example,this paper has explained the physical meaning of the quasi-stationary value condition of the quasi-variational principle in non-conservative single flexible body *** the launch of rocket as an example,it has illustrated the features of"one force for two effects"in a single flexible body *** an example of the extending flexible beam coupled with the spacecraft attitude,it has shown the transition from the single flexible body dynamics to the flexible multi-body ***,a number of related problems are discussed.

关键词： variational principle non-conservative system aerospace dynamics flexible multi-body dynamics single flexible body dynamics

The generalized quasi-variational principles of non-conservative systems with two kinds of variables

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Science China(Physics,Mechanics & Astronomy) 2005年第5期48卷 600-613页

作者： liang lifu LIU Diankui SONG Haiyan School of Civil Engineering Harbin Engineering University Harbin 150001 China School of Civil Engineering Harbin Engineering University Harbin 150001 China School of Civil Engineering Harbin Engineering University Harbin 150001 China

According to the corresponding relations between general forces and general displacements, the balancing and geometrical equations of elasticity are multiplied by the corresponding virtual quantities, integrated with volume and area, and then added algebraically. Proceeding to the next step, by substituting constitutive relation and considering that body force and surface force are both fellow forces, the generalized quasi-variational principles with the two kinds of variables of the first type are established in non-conservative systems. Through substituting another constitutive relation, using similar methods as above, the generalized quasi-variational principles with the two kinds of variables of the second type are established in non-conservative systems. By using the generalized quasi-complementary energy principles with the two kinds of variables of the first type, a method for solving two kinds of variables (internal force and deformation) is given for non-conservative systems of the typical fellow forces.

关键词： non-conservative system, generalized variational principle, two kinds of variables.

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Lagrange方程应用于流体动力学

哈尔滨工程大学学报 2018年第1期39卷 33-39页

作者：梁立孚周平哈尔滨工程大学航天与建筑工程学院黑龙江哈尔滨150001 黑龙江科技大学机械工程学院黑龙江哈尔滨150022

如何将Lagrange方程应用于流体动力学的问题是一个理论研究的难题。按照从变分学的基本理论研究做起的思想,本文应用变导的概念和运算法则,通过研究Lagrange方程中求导的性质,逐步地将Lagrange方程应用于理想流体动力学。按照从变分学... 详细信息

如何将Lagrange方程应用于流体动力学的问题是一个理论研究的难题。按照从变分学的基本理论研究做起的思想,本文应用变导的概念和运算法则,通过研究Lagrange方程中求导的性质,逐步地将Lagrange方程应用于理想流体动力学。按照从变分学的基本理论研究做起的思想,本文应用Lagrange-Hamilton体系,即非保守系统的Lagrange方程是非保守系统的Hamilton型拟变分原理的拟驻值条件,由不可压缩黏性流体动力学的Hamilton型拟变分原理推导出不可压缩黏性流体动力学的Lagrange方程,进而应用不可压缩黏性流体动力学的Lagrange方程推导出不可压缩黏性流体动力学的控制方程。探讨将Lagrange方程应用于可压缩黏性流体动力学问题中,推导出可压缩黏性流体动力学的控制方程。本文解决了如何将Lagrange方程应用于流体动力学的问题。

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

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非保守系统的Lagrange方程

哈尔滨工程大学学报 2017年第3期38卷 452-459页

作者：周平梁立孚哈尔滨工程大学机电工程学院黑龙江哈尔滨150001 黑龙江科技大学机械工程学院黑龙江哈尔滨150022 哈尔滨工程大学航天与建筑工程学院黑龙江哈尔滨150001

如何将Lagrange方程应用于连续介质动力学,一直是学术界关注的理论课题。如何将Lagrange方程应用于非保守连续介质动力学的问题的研究难度更大。本文应用Lagrange-Hamilton体系,非保守系统的Lagrange方程是非保守系统的Hamilton型拟变... 详细信息

如何将Lagrange方程应用于连续介质动力学,一直是学术界关注的理论课题。如何将Lagrange方程应用于非保守连续介质动力学的问题的研究难度更大。本文应用Lagrange-Hamilton体系,非保守系统的Lagrange方程是非保守系统的Hamilton型拟变分原理的拟驻值条件,成功地将Lagrange方程应用于非保守连续介质动力学。进而应用非保守系统的Lagrange方程推导出非保守连续介质动力学的控制方程,为研究非保守连续介质动力学开辟了一条新的有效途径。

关键词：连续介质动力学 Lagrange方程非保守系统拟变分原理拟驻值条件 Lagrange-Hamilton体系