Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference

1994 ◽  
Vol 4 (1) ◽  
pp. 221-251 ◽  
Author(s):  
T. J. Bridges
Keyword(s):  
Spatial Structure ◽  
Water Waves ◽  
Three Dimensional ◽  
Frame Of Reference ◽  
Moving Frame

Nonlinear cellular motions in Poiseuille channel flow

1974 ◽  
Vol 64 (2) ◽  
pp. 319-346 ◽  
Author(s):  
J.-P. Zahn ◽  
Juri Toomre ◽  
E. A. Spiegel ◽  
D. O. Gough
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Infinite System ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Single Mode ◽  
Frame Of Reference ◽  
Moving Frame ◽  
System Of Equations ◽  
Plane Poiseuille Flow

We expand the equations describing plane Poiseuille flow in Fourier series in the co-ordinates in the plane parallel to the bounding walls. There results an infinite system of equations for the amplitudes, which are functions of time and of the cross-stream co-ordinate. This system is drastically truncated and the resulting set of equations is solved accurately by a finite difference method. Three truncations are considered: (I) a single mode with dependence only on the downstream co-ordinate and time, (II) the mode of (I) plus its first harmonic, (III) a single three-dimensional mode. For all three cases, for a variety of initial conditions, the solutions evolve to a steady state as seen in a particular moving frame of reference. No runaways are encountered.

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.

Effect of Ability on Twisting Techniques in Forward Somersaults on the Trampoline

1995 ◽  
Vol 11 (3) ◽  
pp. 267-287 ◽  
Author(s):  
Ross H. Sanders
Keyword(s):  
Dimensional Analysis ◽  
Twist Angle ◽  
Three Dimensional ◽  
Frame Of Reference ◽  
Flexion Angle ◽  
Lateral Flexion ◽  
Analysis Techniques ◽  
Half Twist

This study was designed to investigate the effect of ability on technique in the forward somersault with half twist (Barani) and the forward somersault with one and one half twists (Rudi) on the trampoline. Eleven trampolinists ranging in ability from elite (national representative) to early intermediate (regional representative) were analyzed using three-dimensional analysis techniques. Cumulative twist angle, rate of twist, angle of tilt of the twist axis, chest rotation, hip angle, and hip lateral flexion angle were measured. Characteristics of the arm actions were also assessed using an internal frame of reference. To generate twist in the Baranis, trampolinists tilted the axis between 5° and 14°; the amount of tilt was inversely related to ability (p < .05). In the Rudis, subjects tilted the axis between 15° and 23° using more asymmetrical arm actions and larger and more rapid hip extensions, hip lateral flexions, and chest rotations than in the Baranis. The timing and magnitude of the actions differed among the subjects and were related to ability.

scholarly journals A short geostatistical study of the three-dimensional spatial structure of fumonisins in stored maize

2010 ◽  
Vol 3 (1) ◽  
pp. 95-103 ◽  
Author(s):  
M. Rivas Casado ◽  
D. Parsons ◽  
N. Magan ◽  
R. Weightman ◽  
P. Battilani ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Spatial Structure ◽  
Spatial Correlation ◽  
Three Dimensional ◽  
Sample Collection ◽  
Data Set ◽  
Research Areas ◽  
Geostatistical Approach ◽  
Sampling Protocols ◽  
Current Sample

The heterogeneous three-dimensional spatial distribution of mycotoxins has proven to be one of the main limitations for the design of effective sampling protocols. Current sample collection protocols for mycotoxins have been designed to estimate the mean concentration and fail to characterise the spatial distribution of the mycotoxin concentration due to the aggregation of the incremental samples. Geostatistical techniques have been successfully applied to overcome similar problems in many research areas. However, little work has been developed on the use of geostatistics for the design of sampling protocols for mycotoxins. This paper focuses on the analysis of the two and three-dimensional spatial structure of fumonisins B1 (FB1) and B2 (FB2) in maize in a bulk store using a geostatistical approach and on how results help determine the number and location of incremental samples to be collected. The spatial correlation between FB1 and FB2, as well as between the number of kernels infected and the level of contamination was investigated. For this purpose, a bed of maize was sampled at different depths to generate a unique three-dimensional data set of FB1 and FB2. The analysis found no clear evidence of spatial structure in either the two-dimensional or three-dimensional analyses. The number of Fusarium infected kernels was not a good indicator for the prediction of fumonisin concentration and there was no spatial correlation between the concentrations of the two fumonisins.

Analysis of the Effect of Multirow and Multipassage Aerodynamic Interaction on the Forced Response Variation in a Compressor Configuration—Part I: Aerodynamic Excitation

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Harald Schoenenborn
Keyword(s):  
Three Dimensional ◽  
Forced Response ◽  
Frame Of Reference ◽  
Aerodynamic Damping ◽  
Aerodynamic Interaction ◽  
Blade Row ◽  
Random Mistuning ◽  
Compressor Map ◽  
Response Variation ◽  
Turbomachinery Design

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms, Tyler–Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing. It was recently shown in literature that in multirow configurations, not only the next but also the next but one blade row is very important as it may create a large circumferential forcing variation, which is fixed in the rotating frame of reference. In the present paper, a study of these effects is performed on the basis of a quasi three-dimensional (3D) multirow and multipassage compressor configuration. For the analysis, a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler–Sofrin modes and not to blade-to-blade variation in the steady flow field. The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map, the blade-to-blade forcing variation may change significantly. In addition, multirow flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping. The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

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