scholarly journals On the Deformation Retract of Eguchi-Hanson Space and Its Folding

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
H. Rafat ◽  
Nasr Ahmed
Keyword(s):  
Deformation Retract ◽  
Lagrangian Equations

We introduce the deformation retract of the Eguchi-Hanson space using Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The deformation retract of the Eguchi-Hanson space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced.

The minimum deformation retract on the wormhole spacetime

2020 ◽  
Vol 17 (13) ◽  
pp. 2050198
Author(s):  
M. Abu-Saleem
Keyword(s):  
Line Element ◽  
Geometric Topology ◽  
Deformation Retract ◽  
Lagrangian Equations ◽  
Minimum Deformation

In this paper, we investigate the topology of a wormhole from the viewpoint of the theory of retracting and var-folding. We deduce the equatorial geodesics on the line element of the wormhole and discuss the minimum deformation retract related to this space. Using the Lagrangian equations we find that there is a type of minimum retraction of a wormhole with associated topology. We also extend the result to the [Formula: see text]-dimensional wormhole and show that the end limit of var-folding is 0-dimensional wormhole and obtain the relation between limit var-folding and limit retraction. We find a new application in geometric topology and astrophysics.

scholarly journals On the Deformation Retract of Kerr Spacetime and Its Folding

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
H. Rafat
Keyword(s):  
Kerr Spacetime ◽  
Deformation Retract ◽  
Lagrangian Equations ◽  
Kerr Space

The deformation retract of the Kerr spacetime is introduced using Lagrangian equations. The equatorial geodesics of the Kerr space have been discussed. The retraction of this space into itself and into geodesics has been presented. The deformation retract of this space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced.

Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

2013 ◽  
Author(s):  
Friedhelm Waldhausen ◽  
Bjørn Jahren ◽  
John Rognes
Keyword(s):  
Main Tool ◽  
Homotopy Equivalence ◽  
Classifying Space ◽  
Deformation Retract ◽  
Simplicial Sets ◽  
Full Proof

Since its introduction by the author in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing the author's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a “desingularization,” improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

Functional and Constructive Optimization of a Serial-Modular Industrial Robot Implemented within a Single Purpose Flexible Manufacturing Cell

2012 ◽  
Vol 186 ◽  
pp. 239-246
Author(s):  
Silviu Mihai Petrişor ◽  
Ghiţă Bârsan
Keyword(s):  
Flexible Manufacturing ◽  
Degrees Of Freedom ◽  
Industrial Robot ◽  
Kinematic Chain ◽  
Chain Structure ◽  
Calculation Algorithm ◽  
Flexible Manufacturing Cell ◽  
Manufacturing Cell ◽  
Lagrangian Equations ◽  
Selection Of

The authors of this paper aim to highlight the basic design of a flexible manufacturing cell destined for the final processing of water radiators used for AAVs, cell serviced by a serial modular industrial robot possessing in its kinematic chain structure three degrees of freedom, RRT SIL type. The paper outlines the concept, calculation and design of the (MRB) rotation module at the studied industrial robot’s base and of the (MT) translation module of the prehension device attached to the robotic arm. Depending on the organological elements that are part of the MRB rotation module and based on a rigorous dynamic study performed on robotic modules, modeling conducted with the help of Lagrangian equations of the second kind, a dynamic-organological calculation algorithm was obtained for the selection of the appropriate driving servomotor necessary to putting the rotation movable system into service. The last part of the paper deals with the flexible manufacturing cell, together with the calculations related to profitability, economy and investment return duration, following the implementation of the RRT SIL-type industrial robot.

Experimental and Numerical Investigation of a Large Cylindrical Oil-Fired Combustor

1983 ◽  
Author(s):  
F. M. ElMahallawy ◽  
E. E. Khalil ◽  
O. Abdel Aal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Gas Phase ◽  
Combustion Model ◽  
Steam Boiler ◽  
Discrete Ordinate ◽  
Radiation Model ◽  
Droplet Motion ◽  
Transfer Rates ◽  
Lagrangian Equations

The present work presents measurements of velocity, temperature and heat transfer rates carried out on a segmented water-cooled cylindrical oil-fired flame tube typical of a 0.56 kg/s packaged fire-tube steam boiler. A prediction procedure, that solves the conservation equations of the various entities, was successfully used to produce computed velocities, temperatures and heat flux distributions. A two-equation turbulence model, a combustion model and a discrete ordinate radiation model were used to approximate the various characteristics of the flow. The combustion model solved the Eulerian equations of the gas phase, and the Lagrangian equations of the droplet motion, heating, evaporation and combustion.

Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy

2018 ◽  
Vol 233 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Duy-Chinh Nguyen
Keyword(s):  
Kinetic Energy ◽  
Torsional Vibration ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Tuned Mass Damper ◽  
Optimal Parameters ◽  
Lagrangian Equations ◽  
Tuning Ratio ◽  
Mass Damper

In this paper, an analytical method is presented to determine the optimal parameters of the symmetric tuned mass damper, such as the ratio between natural frequency of tuned mass damper and shaft (tuning ratio) and the ratio of the viscous coefficient of tuned mass damper (damping ratio). The optimal parameters of tuned mass damper are applied to reduce the torsional vibration of the shaft based on consideration of the vibration duration and stability criterion. The dynamic equations of the shaft are provided via Lagrangian equations, and the optimal parameters of tuned mass damper are derived by using the principle of minimum kinetic energy. Analytical and numerical examples are implemented to verify the reliability of the proposed method. The analytical and numerical results indicate that the optimal parameters of tuned mass damper have significant effects in the torsional vibration reduction of the shaft.

Vibrations Analysis for Gun Systems by Multibody Dynamics

1999 ◽  
Author(s):  
Deshi Wang ◽  
Renbin Xiao ◽  
Guangyao Ouyang
Keyword(s):  
Multibody Dynamics ◽  
Maximum Amplitude ◽  
Rigid Bodies ◽  
Lagrangian Equations ◽  
Structure Vibration

Abstract The multi-rigid-bodies model for the single barrel gun has been developed and the structure vibration of the gun has been analyzed though Lagrangian equations reduced by the software on microcomputer. It is shown that the deck stiffness is significant in the effect of the gun vibration, and then that design of a suitable equilibrium equipment and design of the elastic connection axle to increasing the flexibility in pitching movement can effectively decrease the vibration amplitudes of the tube end. The maximum amplitude, for example, could decay to ten percent of that when the measures mentioned above are adopted. It also indicates that entirely removing the vibration is impossible except relevant vibration absorbing measures are adopted. The method and results are also significant in checking the motions of the mechanisms designed in the guns.

Lagrangian equations of motion. Conservation laws

2020 ◽  
pp. 156-174
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Conservation Laws ◽  
Coordinate Transformation ◽  
Virial Theorem ◽  
Equations Of Motion ◽  
Electromechanical System ◽  
Interacting Particles ◽  
Integral Of Motion ◽  
Lagrangian Functions ◽  
Lagrangian Equations

This chapter addresses the invariance of the Lagrangian equations of motion under the coordinate to transformation, the transformation of the energy and generalised momenta under the coordinate transformation. The integrals of motion for a particle moving in the field with a given symmetry to the Noether’s theorem, the Lagrangian functions, and the Lagrangian equations of motion for the electromechanical system. The authors also discuss the influence of constraints and friction on the motion of a system, the virial theorem and its generalization in the presents of a magnetic field, and an additional integral of motion for a system of three interacting particles.

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