Two-Dimensional Transient Motion and Flutter of a Wing Having Four Degrees of Freedom

1952 ◽  
Vol 19 (8) ◽  
pp. 540-542
Author(s):  
HERBERT REISMANN ◽  
GILBERT C. BEST
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensional ◽  
Transient Motion

scholarly journals Thermos Array: Two-Dimensional Sparse Array with Reduced Mutual Coupling

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Lei Sun ◽  
Minglei Yang ◽  
Baixiao Chen
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Mutual Coupling ◽  
Doa Estimation ◽  
Two Dimensional ◽  
Spatial Smoothing ◽  
Planar Arrays ◽  
Half Wavelength ◽  
Planar Array ◽  
Small Spacing

Sparse planar arrays, such as the billboard array, the open box array, and the two-dimensional nested array, have drawn lots of interest owing to their ability of two-dimensional angle estimation. Unfortunately, these arrays often suffer from mutual-coupling problems due to the large number of sensor pairs with small spacing d (usually equal to a half wavelength), which will degrade the performance of direction of arrival (DOA) estimation. Recently, the two-dimensional half-open box array and the hourglass array are proposed to reduce the mutual coupling. But both of them still have many sensor pairs with small spacing d, which implies that the reduction of mutual coupling is still limited. In this paper, we propose a new sparse planar array which has fewer number of sensor pairs with small spacing d. It is named as the thermos array because its shape seems like a thermos. Although the resulting difference coarray (DCA) of the thermos array is not hole-free, a large filled rectangular part in the DCA can be facilitated to perform spatial-smoothing-based DOA estimation. Moreover, it enjoys closed-form expressions for the sensor locations and the number of available degrees of freedom. Simulations show that the thermos array can achieve better DOA estimation performance than the hourglass array in the presence of mutual coupling, which indicates that our thermos array is more robust to the mutual-coupling array.

Monkey superior colliculus represents rapid eye movements in a two-dimensional motor map

1993 ◽  
Vol 69 (3) ◽  
pp. 965-979 ◽  
Author(s):  
K. Hepp ◽  
A. J. Van Opstal ◽  
D. Straumann ◽  
B. J. Hess ◽  
V. Henn
Keyword(s):  
Eye Movements ◽  
Superior Colliculus ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Eye Position ◽  
Two Dimensional ◽  
Vestibular Nystagmus ◽  
Rapid Eye Movements ◽  
Q Model

1. Although the eye has three rotational degrees of freedom, eye positions, during fixations, saccades, and smooth pursuit, with the head stationary and upright, are constrained to a plane by ListingR's law. We investigated whether Listing's law for rapid eye movements is implemented at the level of the deeper layers of the superior colliculus (SC). 2. In three alert rhesus monkeys we tested whether the saccadic motor map of the SC is two dimensional, representing oculocentric target vectors (the vector or V-model), or three dimensional, representing the coordinates of the rotation of the eye from initial to final position (the quaternion or Q-model). 3. Monkeys made spontaneous saccadic eye movements both in the light and in the dark. They were also rotated about various axes to evoke quick phases of vestibular nystagmus, which have three degrees of freedom. Eye positions were measured in three dimensions with the magnetic search coil technique. 4. While the monkey made spontaneous eye movements, we electrically stimulated the deeper layers of the SC and elicited saccades from a wide range of initial positions. According to the Q-model, the torsional component of eye position after stimulation should be uniquely related to saccade onset position. However, stimulation at 110 sites induced no eye torsion, in line with the prediction of the V-model. 5. Activity of saccade-related burst neurons in the deeper layers of the SC was analyzed during rapid eye movements in three dimensions. No systematic eye-position dependence of the movement fields, as predicted by the Q-model, could be detected for these cells. Instead, the data fitted closely the predictions made by the V-model. 6. In two monkeys, both SC were reversibly inactivated by symmetrical bilateral injections of muscimol. The frequency of spontaneous saccades in the light decreased dramatically. Although the remaining spontaneous saccades were slow, Listing's law was still obeyed, both during fixations and saccadic gaze shifts. In the dark, vestibularly elicited fast phases of nystagmus could still be generated in three dimensions. Although the fastest quick phases of horizontal and vertical nystagmus were slower by about a factor of 1.5, those of torsional quick phases were unaffected. 7. On the basis of the electrical stimulation data and the properties revealed by the movement field analysis, we conclude that the collicular motor map is two dimensional. The reversible inactivation results suggest that the SC is not the site where three-dimensional fast phases of vestibular nystagmus are generated.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Rapid Measurement and Identification Method for the Geometric Errors of CNC Machine Tools

2019 ◽  
Vol 9 (13) ◽  
pp. 2701 ◽  
Author(s):  
Li ◽  
Yang ◽  
Gao ◽  
Su ◽  
Wei ◽  
...  
Keyword(s):  
Error Compensation ◽  
Machine Tools ◽  
Degrees Of Freedom ◽  
Cnc Machine Tools ◽  
Geometric Errors ◽  
Two Dimensional ◽  
Cnc Machine ◽  
Angle Sensor ◽  
Identification Method ◽  
Measuring Machine

Error compensation technology offers a significant means for improving the geometric accuracy of CNC machine tools (MTs) as well as extending their service life. Measurement and identification are important prerequisites for error compensation. In this study, a measurement system, mainly composed of a self-developed micro-angle sensor and an L-shape standard piece, is proposed. Meanwhile, a stepwise identification method, based on an integrated error model, is established. In one measurement, four degrees-of-freedom errors, including two-dimensional displacement and two-dimensional angle of a linear guideway, can be obtained. Furthermore, in accordance with the stepwise identification method, the L-shape standard piece is placed in three different planes, so that the measurement and identification of all 21 geometric errors can be implemented. An experiment is carried out on a coordinate measuring machine (CMM) to verify the system. The residual error of the angle error, translation error and squareness error are 1.5″, 2 μm and 3.37″, respectively, and these are compared to the values detected by a Renishaw laser interferometer.

scholarly journals Efficient Two-Dimensional Direction Finding Algorithm for Rectilinear Sources Under Unknown Mutual Coupling

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1914
Author(s):  
Jian Xie ◽  
Qiuping Wang ◽  
Yuexian Wang ◽  
Xin Yang
Keyword(s):  
Degrees Of Freedom ◽  
Mutual Coupling ◽  
Array Signal Processing ◽  
Elevation Angle ◽  
Doa Estimation ◽  
Two Dimensional ◽  
Rank Reduction ◽  
Communication Signals ◽  
Estimation Performance ◽  
Direction Cosines

Digital communication signals in wireless systems may possess noncircularity, which can be used to enhance the degrees of freedom for direction-of-arrival (DOA) estimation in sensor array signal processing. On the other hand, the electromagnetic characteristics between sensors in uniform rectangular arrays (URAs), such as mutual coupling, may significantly deteriorate the estimation performance. To deal with this problem, a robust real-valued estimator for rectilinear sources was developed to alleviate unknown mutual coupling in URAs. An augmented covariance matrix was built up by extracting the real and imaginary parts of observations containing the circularity and noncircularity of signals. Then, the actual steering vector considering mutual coupling was reparameterized to make the rank reduction (RARE) property available. To reduce the computational complexity of two-dimensional (2D) spectral search, we individually estimated y-axis and x-axis direction-cosines in two stages following the principle of RARE. Finally, azimuth and elevation angle estimates were determined from the corresponding direction-cosines respectively. Compared with existing solutions, the proposed method is more computationally efficient, involving real-valued operations and decoupled 2D spectral searches into twice those of one-dimensional searches. Simulation results verified that the proposed method provides satisfactory estimation performance that is robust to unknown mutual coupling and close to the counterparts based on 2D spectral searches, but at the cost of much fewer calculations.

Fictitious Domain Solution of Frequency Response Problems

1999 ◽  
Author(s):  
Sudarsanam Chellappa ◽  
Giuseppe C. A. DeRose ◽  
Alejandro R. Diaz
Keyword(s):  
Frequency Response ◽  
Meshless Method ◽  
Degrees Of Freedom ◽  
Convergence Rates ◽  
Iterative Solvers ◽  
Fictitious Domain ◽  
Solution Technique ◽  
Two Dimensional ◽  
Solution Strategy ◽  
Arbitrary Geometries

Abstract This paper discusses an alternative solution strategy for frequency response problems in elasticity. This strategy uses a meshless method, derived in a periodic domain setting, extended to allow the analysis of arbitrary geometries with the use of a fictitious domain. This solution technique is designed to solve problems with a large number of degrees of freedom and it requires the use of iterative solvers where preconditioning is necessary for reasonable convergence rates. Two dimensional examples illustrating this approach are provided.

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

2013 ◽  
Vol 13 (5) ◽  
pp. 1309-1329 ◽  
Author(s):  
Laura Lazar ◽  
Richard Pasquetti ◽  
Francesca Rapetti
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Schur Complement ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Flow Past A Cylinder ◽  
Accuracy Study

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

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