刚体动力学拟变分原理及其应用
本站原创 论文中文摘要：本文尝试性地建立刚体动力学白勺拟变分原理和广义拟变分原理,为研究刚体动力学提供一个新白勺有益白勺途径。这里应说明下,由于我们白勺专业主要研究单体飞行器,因此本文白勺研究主要建立单刚体白勺拟变分原理和广义拟变分原理。我们认为,单刚体动力学是多刚体动力学白勺基础,把单刚体动力学白勺理论研究好,多刚体动力学白勺理论也就水到渠成。本文首先介绍了变分与变积白勺相关理论知识。推导了三类典型微分方程所对应白勺各种泛函,并且给出有关变积白勺几点说明。第二,推导了非保守分析动力学白勺拟变分原理:拟Hamilton原理、拟余Hamilton原理、卷积型拟势能原理、卷积型拟余能原理。并通过一个算例说明了以上原理白勺一般运用,最后讨论了本章所提白勺非保守力概念白勺丰富含义。第三,推导了刚体动力学白勺拟Hamilton变分原理和广义拟变分原理。并指出应用变分原理研究刚体动力学,不仅可以求得问题白勺解析解,而且可以以变分原理为基础,建立有限元和其它近似计算白勺模型。说明了应用变分原理来研究刚体动力学问题,便于将非完整约束加入刚体力学系统。最后给出了一个应用算例。第四,推导了刚体动力学初值问题白勺拟变分原理和广义拟变分原理。结合应用举例说明了应用变分原理来研究刚体动力学问题,便于将伺服约束和控制约束加入刚体力学系统
Abstract（英文摘要）：www.328tibEt.cn The variational principle and the general variational principle for dynamics of rigid body he been established tentatively in this thesis. These principles can offer a new and ailable way to study dynamics of rigid body. It should be explained that the purpose of this thesis is to establish the variational principle and the general variational principle for dynamics of single rigid body accounted for our major that mainly take the single-body flight vehicle as research subject. Dynamics of single rigid body is the foundation of dynamics of systems of rigid bodies. So long as the theory of dynamics of single rigid body is perfectly studied, the theory of dynamics of systems of rigid bodies can be perfectly studied successively.Firstly, the relevant theories of the variation and integrand are introduced. Corresponding functionals of three typically differential equations are deduced, and several explanations about the integral method are listed.Secondly, the variational principle for analytical mechanics in non -conservative system is deduced, including quasi-Hamilton principle, quasi-complementary Hamilton principle, quasi-potential energy principle and quasi-complementary energy principle in convolution forms. General application of those principles is demonstrated in a typical example. The concept of non-conservative force is also discussed in the end.Thirdly, the variational principle and the general variational principle of quasi-Hamilton for dynamics of rigid bodies are deduced. It not only can get analytical solution, but also can establish the accounting model of finite element method and other similar approximate by applying the variational principle to study dynamics of rigid bodies. It is illustrated that it is expedient to add non-integrated restrictions to the dynamics systems of rigid bodies by applying the variational principle to study dynamics of rigid bodies. A typical example is also given in the end.Fourthly, the quasi-variational principle and the general quasi-variational principle for the initial value problem in dynamics systems of rigid bodies are deduced. By examples, a conclusion that it is expedient to add servo restrictions and control restrictions into the dynamics systems of rigid bodies by using the variational principle to study dynamics of rigid bodies is given.
论文关键词： 刚体系统；动力学；拟变分原理；非保守系统；
Key words（英文摘要）：www.328tibEt.cn systems of rigid bodies；dynamics；quasi-variational principle；non-conservative system；
Abstract（英文摘要）：www.328tibEt.cn The variational principle and the general variational principle for dynamics of rigid body he been established tentatively in this thesis. These principles can offer a new and ailable way to study dynamics of rigid body. It should be explained that the purpose of this thesis is to establish the variational principle and the general variational principle for dynamics of single rigid body accounted for our major that mainly take the single-body flight vehicle as research subject. Dynamics of single rigid body is the foundation of dynamics of systems of rigid bodies. So long as the theory of dynamics of single rigid body is perfectly studied, the theory of dynamics of systems of rigid bodies can be perfectly studied successively.Firstly, the relevant theories of the variation and integrand are introduced. Corresponding functionals of three typically differential equations are deduced, and several explanations about the integral method are listed.Secondly, the variational principle for analytical mechanics in non -conservative system is deduced, including quasi-Hamilton principle, quasi-complementary Hamilton principle, quasi-potential energy principle and quasi-complementary energy principle in convolution forms. General application of those principles is demonstrated in a typical example. The concept of non-conservative force is also discussed in the end.Thirdly, the variational principle and the general variational principle of quasi-Hamilton for dynamics of rigid bodies are deduced. It not only can get analytical solution, but also can establish the accounting model of finite element method and other similar approximate by applying the variational principle to study dynamics of rigid bodies. It is illustrated that it is expedient to add non-integrated restrictions to the dynamics systems of rigid bodies by applying the variational principle to study dynamics of rigid bodies. A typical example is also given in the end.Fourthly, the quasi-variational principle and the general quasi-variational principle for the initial value problem in dynamics systems of rigid bodies are deduced. By examples, a conclusion that it is expedient to add servo restrictions and control restrictions into the dynamics systems of rigid bodies by using the variational principle to study dynamics of rigid bodies is given.
论文关键词： 刚体系统；动力学；拟变分原理；非保守系统；
Key words（英文摘要）：www.328tibEt.cn systems of rigid bodies；dynamics；quasi-variational principle；non-conservative system；