This paper deduces the mathematical model of a single-inverted pendulum system by Lagrange equation and designs its controller by the adaptive fuzzy method, later, combining its model and controller in Matlab simulation and operating it.
Therefore, the higher-order differential equations of motion of the holonomic system are a complement to the second-order differential equations of motion, including Newtonian kinetic equations and the traditional Lagrange equations, Nielsen equations and Appell equations.
By using higher order Lagrange equations of holonomic mechanical system,higher order Hamilton's canonical equations of holonomic mechanical system are obtained,by which the higher order cyclic integral and the higher order generalized energy integral of holonomic potential mechanical system are obtained,and the physical meaning of higher order Hamilton's function is explained.
Starting from Newtonian kinetic equations of a particle system, the energy of higher order_velocity of the system is introduced; higher_order Lagrange equations, higher_order Nielsen equations and higher_order Appell equations of a holonomic mechanical system are derived, from which we prove that the three kinds of higher_order differential equations of motion of the holonomic system are equivalent to each other.
Lagrangian mechanics on Khler manifolds were discussed,and the complex mathematical aspects of Lagrangian operator,Lagrange's equation,the action functional,Hamilton's principle and Hamilton's equation,and so on were given.
In this paper,the Lagrange's Equation is used to establish the dynamic equation of a linear viscoelastic simple manipulator rotating in a plane,the effect of vlscoelastic property on the vibration of manipulator's end and the interaction between elastic vibration and rigid motion are analysed.
Secondly, the humanoid robot platform is simplified, and on the basis of ignoring thecoupling effect between the frontal motion and the lateral motion, the frontal and the lateraldynamics models of humanoid robot are built up using Lagrange method.
In this paper w e analyze the dynamics of rotary inverted pendulum system and derive its mode l based on Lag rang e method. Then the linear quadratic optimal control str ateg y is applied to desig n the controller. The effectiveness of the proposed method is proved by balancing the pendulum at the inverted state successfully on the Windows 2000platform.
The coefficients of the time-dependent power series for the velocity potential, the equation of the free surface, and the pressure on the solid are determined, allowing for all the terms in the Cauchy-Lagrange equation.
The Euler-Lagrange equation for the polarization P is solved by the direct variational method.
The electric field produced by charges on electrodes is taken into account (with allowance for the screening of the charges in the metals) in the free energy functional and in the Euler-Lagrange equation for the film polarization.
Analogs of the Lagrange equation for particles evolving in a space of fractal dimension are obtained.
In the latter case the fractional integrodifferential formalism is utilized, and a new principle for devising a fractal theory, viz., a generalized principle of least action, is proposed and used to obtain the corresponding Lagrange equation.
Reminiscent of the selfdual Yang-Mills equations, they are not derived from the fact that they are critical points (i.e., from the corresponding Euler-Lagrange equations) but from being zeroes of the corresponding non-negative Lagrangians.
Consideration was given to control of the plant obeying the second-order Lagrange equations.
The elements of this set are represented by the systems obeying the Lagrange equations of the second kind and having also bounded inertial characteristics and generalized forces.
Lagrange equations for a system of bubbles of varying radii in a liquid of small viscosity
Using the basic equations of hydromechanics and also the Lagrange equations of the second kind, expressions are derived for the force acting between a liquid and a vapor bubble growing within it.
The present article gives below a method for calculating the coagulation process of particles in a nozzle using the Lagrange method, and analyzes the results of electronic-computer calculations, carried out using both of the above-discussed methods.
Computations are performed by a finite-difference Lagrange method according to a program for plane motions of a continuous medium  by using a volume artificial viscosity of Neumann-Richtmayer type .
The experiments are numerically simulated by the two-dimensional Lagrange method.
On the basis of the Lyapunov-Lagrange method, we propose a method for searching for an optimal control strategy depending on known components of the state vector.
This result fills the gap between the conditions needed by the energy-Casimir method and by the energy-Lagrange method.