Bond Graphs and Lagrange Equations as Aids in Analytical Studies of Electro-Mechanical Systems

2012 ◽  
Vol 45 (2) ◽  
pp. 398-403
Author(s):  
Dean Karnopp
Keyword(s):  
Mechanical Systems ◽  
Lagrange Equations ◽  
Bond Graphs ◽  
Analytical Studies

scholarly journals Alternative Lagrangians obtained by scalar deformations

2020 ◽  
Vol 17 (04) ◽  
pp. 2050050
Author(s):  
Oana A. Constantinescu ◽  
Ebtsam H. Taha
Keyword(s):  
Force Field ◽  
Differentiable Function ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Initial System ◽  
Lagrange Equations ◽  
Necessary And Sufficient ◽  
Equations Of Motions

We study mechanical systems that can be recast into the form of a system of genuine Euler–Lagrange equations. The equations of motions of such systems are initially equivalent to the system of Lagrange equations of some Lagrangian [Formula: see text], including a covariant force field. We find necessary and sufficient conditions for the existence of a differentiable function [Formula: see text] such that the initial system is equivalent to the system of Euler–Lagrange equations of the deformed Lagrangian [Formula: see text].

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

Aplicación del formalismo de Lagrangianos Controlados en la regulación de velocidad del motor de inducción trifásico

2021 ◽  
Author(s):  
◽  
Yaima González Acosta
Keyword(s):  
Mechanical Systems ◽  
Electrical Machines ◽  
Lagrangian Formalism ◽  
Control Law ◽  
Lagrange Equations ◽  
Two Phase ◽  
Main Research ◽  
Three Phase ◽  
First Time ◽  
Selection Of

In this work the Controlled Lagrangian Formalism applied to electrical machines is explored for the first time. It begins with an analysis of the purely mechanical systems, once understood, the study is carried out on a two-phase induction motor, this implying a greater degree of complexity because there is no reference that has done it before. Finally, this study is expanded to the three-phase motor, this being the main research object of the project. The main guide used was the Bloch article cite bloch2000controlled on the analysis of mechanical systems. Regarding the procedure, the first thing that is done is the selection of the generalized coordinates, the Lagrangian is proposed and the model is obtained from it through the Euler-Lagrange equations, followed by that the symmetries are identified (which in the case of MI is especially interesting because these symmetries are obvious from the choice of coordinates) and the configuration space is divided into vertical and horizontal directions, the horizontal directions are redefined and the Controlled Lagrangian is proposed. Finally, generalized forces are sought, using Noether's Theorem as support and thus establishing the control law. The development to obtain the Controlled Lagrangian and the control law is done in detail, explaining each step of the procedure and using specific algebraic methods of this formalism that are strongly based on the geometric structure of the variety of configuration. The results obtained are an approach in the direction of Controlled Lagrangians applied electrical machines.

The Usage of Bond Graphs Methodology for Mechanical Systems Designing

2015 ◽  
Vol 816 ◽  
pp. 349-356
Author(s):  
Darina Hroncová ◽  
Alexander Gmiterko ◽  
Tomáš Lipták ◽  
František Menda
Keyword(s):  
Classical Method ◽  
Mechanical Systems ◽  
Dc Motor ◽  
Bond Graph ◽  
Bond Graphs ◽  
Introductory Part ◽  
Definition Of ◽  
Simulation Scheme

The article deals with the issue of the usage bond graphs at modeling of mechanical systems. In contrast with the classical method, where the equations for individual components are created first and then on their basis the simulation scheme is derived, here the described method uses the reverse procedure. In the introductory part of article the bond graph notation is defined and next basic types of multi-ports are explained. The last part consists of definition of port and power bond between ports that are explained on example of DC motor with separate excitation.

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

2009 ◽  
Vol 18 (11) ◽  
pp. 4650-4656 ◽  
Author(s):  
Zhang Ming-Jiang ◽  
Fang Jian-Hui ◽  
Lu Kai ◽  
Zhang Ke-Jun ◽  
Li Yan
Keyword(s):  
Conformal Invariance ◽  
Mechanical Systems ◽  
Conserved Quantity ◽  
Lagrange Equations ◽  
Third Order

scholarly journals Numerical and Dynamic Errors Analysis of Planar Multibody Mechanical Systems With Adjustable Clearance Joints Based on Lagrange Equations and Experiment

2020 ◽  
Vol 15 (8) ◽  
Author(s):  
Hui Li ◽  
Jin Xie ◽  
Wei Wei
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Model ◽  
Mechanical Systems ◽  
Engineering Application ◽  
Lagrange Equations ◽  
Dynamical Equations ◽  
Absolute Deviation ◽  
Clearance Joints ◽  
Dynamic Errors ◽  
Errors Analysis

Abstract For theoretical study and engineering application, it is necessary to provide an accurate and simple dynamical model to simulate the multibody mechanical systems with clearance joints and it is also the subject of this article. Based on Lagrange equations of the first kind, a different numerical methodology, the length and rotation angle of the clearance joints are looked as independent coordinates for the first time, is presented in detail. The slider–crank mechanism, with a single or double adjustable revolute clearance joints, is used as a numerical model. A test rig and a simulink model, fully in accordance with the numerical model, are used to measure the velocity, displacement, and acceleration. The numerical results tally with experimental and simulink results reveal that the new methodology, presented in this paper, provides a correct approach to build the dynamical equations of mechanism with clearance joints. Lyapunov exponent is used to analyze the motion status, chaotic or periodic, of the slider. Based on data points, mean absolute deviation (MAD) is applied to judge the dynamical errors, displacement, velocity, and acceleration, of the slider due to clearance joints. With the help of Lyapunov exponent and MAD, the results indicated that various clearance sizes and drive speeds can change the dynamical behaviors of the slider, which is complex but can be predicted in some way.

Modeling of the dynamics of switching stages of hydromechanical gears based on the Lagrange equations with indefinite multipliers

2020 ◽  
pp. 19-25
Author(s):  
N.N Gorbatenko
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Lagrange Equations ◽  
Concentrated Masses

A procedure is proposed for modeling automobile hydromechanical transmissions, based on representing them in the form of multi-mass mechanical systems and applying the Lagrange equations with indefinite multipliers to derive the equations of motion of concentrated masses. Keywords hydromechanical transmission, clutches, gear shifting, mathematical model, Lagrange equations with indefinite multipliers. [email protected]

Development and Application of a Generalized d’Alembert Force for Multifreedom Mechanical Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 317-326 ◽  
Author(s):  
M. A. Chace ◽  
Y. O. Bayazitoglu
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Lagrange Equations ◽  
Second Order Differential Equations ◽  
Dimensional Version ◽  
Mechanical Networks ◽  
Geometric Effects

A set of expressions termed the generalized d’Alembert force is determined for application to two and three-dimensional dynamic analysis of discrete, nonlinear, multifreedom, constrained, mechanical dynamic systems. These expressions greatly simplify the task of developing a correct set of second order differential equations of motion for mechanical systems which are nonlinear because of large deflections or other geometric effects. They apply to both constrained and unconstrained mechanical systems via the method of Lagrange equations with constraint. The two-dimensional version of the expressions has been successfully applied in a type-varient computer program for the dynamic analysis of mechanical networks, and example problems simulated with this program are discussed.

The Poincaré variational principle in the Lagrange–Poincaré reduction of mechanical systems with symmetry

2019 ◽  
Vol 16 (05) ◽  
pp. 1950068
Author(s):  
S. N. Storchak
Keyword(s):  
Riemannian Manifold ◽  
Variational Principle ◽  
Mechanical Systems ◽  
Scalar Particle ◽  
Orbit Space ◽  
Local Dynamic ◽  
Lagrange Equations ◽  
Smooth Action ◽  
Finite Dimensional ◽  
Dependent Coordinates

The local Lagrange–Poincaré equations (the reduced Euler–Lagrange equations) for the mechanical system describing the motion of a scalar particle on a finite-dimensional Riemannian manifold with a given free isometric smooth action of a compact semi-simple Lie group are obtained. The equations are written in terms of dependent coordinates which are used to represent the local dynamic given on the orbit space of the principal fiber bundle. The derivation of the equations is performed with the help of the variational principle developed by Poincaré for mechanical systems with symmetry.

FRACTIONAL TIME ACTION AND PERTURBED GRAVITY

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 243-247 ◽  
Author(s):  
MADHAT SADALLAH ◽  
SAMI I. MUSLIH ◽  
DUMITRU BALEANU ◽  
EQAB RABEI
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Variational Problems ◽  
Integral Function ◽  
Lagrange Equations ◽  
Action Integral

In this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < α ≤ 1. Two examples are investigated in detail.

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