scholarly journals Characterizations of Adjoint Curves According to Alternative Moving Frame

2022 ◽  
Author(s):  
Ali ÇAKMAK ◽  
Volkan ŞAHİN
Keyword(s):  
Moving Frame ◽  
Adjoint Curves

scholarly journals SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES

2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN
Keyword(s):  
Single Particle ◽  
Inertial Frame ◽  
Quantum States ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Mixed States ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
Momentum Correlation ◽  
Spin Momentum

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

scholarly journals Navier-Stokes and Potential Calculations of Axial Spacing Effect on Vortical and Potential Disturbances and Gust Response in an Axial Compressor

1995 ◽  
Author(s):  
Meng-Hsuan Chung ◽  
Andrew M. Wo
Keyword(s):  
Lower Order ◽  
Spacing Effect ◽  
Axial Compressor ◽  
Interaction Effects ◽  
Moving Frame ◽  
Navier Stokes ◽  
Blade Row ◽  
Vortical Disturbance ◽  
Blade Row Interaction ◽  
Gust Response

The effect of blade row axial spacing on vortical and potential disturbances and gust response is studied for a compressor stator/rotor configuration near design and at high loadings using 2D incompressible Navier-Stokes and potential codes, both written for multistage calculations. First, vortical and potential disturbances downstream of the isolated stator in the moving frame are defined; these disturbances exclude blade row interaction effects. Then, vortical and potential disturbances for the stator/rotor configuration are calculated for axial gaps of 10%, 20%, and 30% chord. Results show that the potential disturbance is uncoupled; the potential disturbance calculated from the isolated stator configuration is a good approximation for that from the stator/rotor configuration for all three axial gaps. The vortical disturbance depends strongly on blade row interactions. Low order modes of vortical disturbance are of substantial magnitude and decay much more slowly downstream than do those of potential disturbance. Vortical disturbance decays linearly with increasing mode except very close to the stator trailing edge. For a small axial gap, lower order modes of both vortical and potential disturbances must be included to determine the rotor gust response.

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

scholarly journals GRAVITATIONAL FIELD OF SPHERICAL BRANES

2008 ◽  
Vol 23 (35) ◽  
pp. 2979-2986
Author(s):  
MERAB GOGBERASHVILI
Keyword(s):  
Black Holes ◽  
Gravitational Field ◽  
Analytic Form ◽  
Gravitational Mass ◽  
Moving Frame ◽  
Coordinate Transformations ◽  
Einstein's Equations ◽  
Five Dimensions ◽  
Physical Fields ◽  
Active Gravitational Mass

The warped solution of Einstein's equations corresponding to the spherical brane in five-dimensional AdS is considered. This metric represents interiors of black holes on both sides of the brane and can provide gravitational trapping of physical fields on the shell. It is found that the analytic form of the coordinate transformations from the Schwarzschild to co-moving frame that exists only in five dimensions. It is shown that in the static coordinates active gravitational mass of the spherical brane, in agreement with Tolman's formula, is negative, i.e. such objects are gravitationally repulsive.

scholarly journals Analysis of dynamics of a vertical cantilever in rotary coupling to the moving frame with movement limiters

2018 ◽  
Vol 241 ◽  
pp. 01021
Author(s):  
Piotr Wolszczak ◽  
Grzegorz Litak ◽  
Krystian Lygas
Keyword(s):  
Mechanical Energy ◽  
Elastic Beam ◽  
Beam Deflection ◽  
Moving Frame ◽  
Nonlinear Phenomena ◽  
Horizontal Distance ◽  
Energy Effect ◽  
Cross Sectional ◽  
Excitation Beam ◽  
Analysis Of Dynamics

The efficiency of the mechanical energy harvesting with the use of vibrating elements can be improved by synchronizing stimulation vibrations and own linear frequencies of systems as well as super or sub harmonics induced by non-linear phenomena. The article presents numerical cross-sectional study of the mechanical system. The system consists of an elastic beam set vertically, which the lower end is fixed in the rotary support, and is stimulated to move in the horizontal axis. The upper end of the beam is free but below its level there are bumpers limiting the free rotation of the beam. Numerical studies took into account the variability of the frequency and amplitude of the excitation beam movement, and horizontal distance between bumpers. Beam deflection was observed, on the basis of which the amount of energy generated by the piezo element was estimated. Nonlinear phenomena and analysis of frequency synchronization of vibrations improving the energy effect of an energy generator are presented.

scholarly journals A Moving Frame Trajectory Tracking Method of a Flying-Wing UAV Using the Differential Geometry

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Flight Control ◽  
Trajectory Tracking ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Dynamic Equations ◽  
Moving Frame ◽  
Moving Frames ◽  
Tracking Method ◽  
Tracking Process

The problem of UAV trajectory tracking is a difficult issue for scholars and engineers, especially when the target curve is a complex curve in the three-dimensional space. In this paper, the coordinate frames during the tracking process are transformed to improve the tracking result. Firstly, the basic concepts of the moving frame are given. Secondly the transfer principles of various moving frames are formulated and the Bishop frame is selected as a final choice for its flexibility. Thirdly, the detailed dynamic equations of the moving frame tracking method are formulated. In simulation, a moving frame of an elliptic cylinder helix is formulated precisely. Then, the devised tracking method on the basis of the dynamic equations is tested in a complete flight control system with 6 DOF nonlinear equations of the UAV. The simulation result shows a satisfactory trajectory tracking performance so that the effectiveness and efficiency of the devised tracking method is proved.

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