查看更多>>摘要：This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it.Firstly,starting from the dynamic equation of the relative motion of particles,we give the Gauss principle of relative mo-tion dynamics.By constructing a compulsion function of relative motion,we prove that at any instant,its real motion minimizes the com-pulsion function under Gaussian variation,compared with the possible motions with the same configuration and velocity but different ac-celerations.Secondly,the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane.Thirdly,the Gauss principle we obtained is expressed as Appell,Lagrange,and Nielsen forms in generalized coordinates.Utilizing Gauss principle,the dynamical equations of relative motion are established.Finally,two rela-tive motion examples also verify the results'correctness.
查看更多>>摘要：In this paper,two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic be-haviors.First of all,according to the first-order approximation method and the stabilization condition of the linear system,one linear feed-back controller is structured to control the chaotic system without time-delay,its chaotic behavior is eliminated and stabilized to its equilib-rium.After that,based on the first-order approximation method,the Lyapunov stability theorem,and the matrix inequality theory,the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium.Finally,two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.
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