Lagrange equation of another class of nonholonomic systems

1991 ◽  
Vol 12 (8) ◽  
pp. 727-732
Author(s):  
Gao Pu-yun ◽  
Guo Zhong-heng
Keyword(s):  
Lagrange Equation ◽  
Nonholonomic Systems

Lagrange equation of a class of nonholonomic systems

1991 ◽  
Vol 12 (5) ◽  
pp. 421-424 ◽  
Author(s):  
Gao Pu-yun ◽  
Guo Zhong-heng
Keyword(s):  
Lagrange Equation ◽  
Nonholonomic Systems

On an Euler-Lagrange equation for color to grayscale conversion

2019 ◽  
Vol 2019 (1) ◽  
pp. 95-98
Author(s):  
Hans Jakob Rivertz
Keyword(s):  
Variational Inequality ◽  
Color Image ◽  
Lagrange Equation ◽  
New Method ◽  
Grayscale Image ◽  
Structure Tensors

In this paper we give a new method to find a grayscale image from a color image. The idea is that the structure tensors of the grayscale image and the color image should be as equal as possible. This is measured by the energy of the tensor differences. We deduce an Euler-Lagrange equation and a second variational inequality. The second variational inequality is remarkably simple in its form. Our equation does not involve several steps, such as finding a gradient first and then integrating it. We show that if a color image is at least two times continuous differentiable, the resulting grayscale image is not necessarily two times continuous differentiable.

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Virtual Work & d’Alembert’s Principle

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Euler Equations ◽  
Virtual Work ◽  
Lagrange Equation ◽  
Classical Mechanics ◽  
Rigid Bodies ◽  
Gibbs Function ◽  
Constraint Force ◽  
Appell Equations ◽  
Jourdain's Principle ◽  
D'alembert's Principle

This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.

Kinematic characteristics of longitudinal double folding wings

2021 ◽  
pp. 1-25
Author(s):  
L. Tiegang ◽  
C. Guoguang ◽  
L. Shuai
Keyword(s):  
Angular Velocity ◽  
Structural Model ◽  
Initial Conditions ◽  
Aerodynamic Force ◽  
Model Simulation ◽  
Lagrange Equation ◽  
Grid Method ◽  
Weapon Systems ◽  
Folding Wing ◽  
Double Folding

ABSTRACT A folding wing is a tactical missile launching device that needs to be miniaturised to facilitate storage, transportation, and launching; save missile and transportation space; and improve the combat capability of weapon systems. This study investigates the aeroelastic characteristics of the secondary longitudinal folding wing during the unfolding process. First, the Lagrange equation is used to establish the structural dynamics model of the folding wing, the kinematics characteristics during the deformation process are analysed, and the unfolding movement of the folding wing is obtained using the dynamic equations in the process. Then, the generalised unsteady aerodynamic force is calculated using the dipole grid method, and the multi-body dynamics equation of the folding wing is obtained. The initial angular velocity required for the deployment of the folding wing is analysed through structural model simulation, and the influence of the initial angular velocity on the opening process is studied. Finally, aeroelastic flutter analysis is performed on the folding wing, and the physical model of the folding wing verified experimentally. Results show that the type of aeroelastic response is sensitive to the initial conditions and the way the folding wing opens.

Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

2020 ◽  
pp. 014233122097417
Author(s):  
Qinghui Du
Keyword(s):  
State Feedback ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Feedback Controller ◽  
Input State ◽  
Time Varying ◽  
Initial State ◽  
State Feedback Controller ◽  
Time Varying Delay ◽  
Varying Delay

The problem of adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations is studied in this paper. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using the input-state scaling technique and an adaptive backstepping control approach. Then, by adopting the switching strategy to eliminate the phenomenon of uncontrollability, the proposed adaptive state-feedback controller can guarantee that the closed-loop system has an almost surely unique solution for any initial state, and the equilibrium of interest is globally asymptotically stable in probability. Finally, the simulation example shows the effectiveness of the proposed scheme.

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