Research On The Quasi-variational Principle For Dynamics Of Rigid Bodies And Their Application

The variational principle and the general variational principle for dynamics of rigid body have been established tentatively in this thesis. These principles can offer a new and available 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.