船只/桥梁多柔体系统碰撞问题求解的Lagrange方程

通过对船只 /桥梁多柔体系统碰撞问题进行具体分析并作适当简化和离散化 ,形成集中质量 -弹簧体系模型 ,针对模型按广义坐标建立拉格朗日微分方程组 ,简述了该方程组的解法 。

Extremum response surface method of reliability analysis on two-link flexible robot manipulator

In order to present a new method for analyzing the reliability of a two-link flexible robot manipulator,Lagrange dynamics differential equations of the two-link flexible robot manipulator were established by using the integrated modal method and the multi-body system dynamics method.By using the Monte Carlo method,the random sample values of the dynamic parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed their displacement,speed and acceleration.On this basis,dynamic stresses and deformations were obtained.By taking the maximum values of the stresses and the deformations as output responses and the random sample values of dynamic parameters as input quantities,extremum response surface functions were established.A number of random samples were then obtained by using the Monte Carlo method and then the reliability was analyzed by using the extremum response surface method.The results show that the extremum response surface method is an efficient and fast reliability analysis method with high-accuracy for the two-link flexible robot manipulator.

Gradient Transformation of Momentum and Single-Valued Vector Potential in Nonrelativistic Dynamics

A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.

Dynamic Analysis of aSelected Spatial One-DOF Linkage Mechanism with Friction in Joints

The dynamic analysis of a one-DOF RSRRR spatial linkage mechanism, including four rotational joints R and one spherical joint S, is presented in the paper. It is assumed that friction occurs in the rotational joints, whereas a spherical joint can be treated as an ideal one. The mechanism in the form of a closed-loop kinematic chain was divided by cut joint technique into two open-loop kinematic chains in place of the spherical joint. Joint coordinates and homogeneous transformation matrices were used to describe the geometry of the system. Equations of the chains＇ motion were derived using formalism of Lagrange equations. Cut joint constraints and reaction forces, acting in the cutting place---i.e, in the spherical joint, have been introduced to complete the equations of motion. As a consequence, a set of differential-algebraic equations has been obtained. In order to solve these equations, a procedure based on differentiation twice of the formulated constraint equations with respect to time has been applied. In order to determine values of friction torques in the rotational joints in each integrating step of the equations of motion, joint forces and torques were calculated using the recursive Newton-Euler algorithm taken from robotics. For the requirements of the method, a model of a rotational joint has been developed. Some examples of results of the numerical calculations made have been presented in the conclusions of the paper.

Robust nonlinear control of spacecraft formation flying using constraint forces

A robust nonlinear control method is presented for spacecraft precise formation flying.With the constraint forces and consid-ering nonlinearity and perturbations,the problem of the formation keeping is changed to the Lagrange systems with the holonomic constraints and the differential algebraic equations (DAE).The nonlinear control laws are developed by solving the DAE.Because the traditional numerical solving methods of DAE are very sensitive to the various errors and the resulting con-trol laws are not robust in engineering application,the robust control law designed method is further developed by designing the correct coefficients to correct the errors of the formation array constraints.A numeral study simulated the robustness of this method for the various errors in the formation flying mission,including the initial errors of spacecraft formation,the reference satellite orbit determination errors,the relative perturbation forces model errors,and so on.