Generalized Fermi–Walker derivative and non-rotating frame

2017 ◽  
Vol 14 (09) ◽  
pp. 1750131 ◽  
Author(s):  
Ayşenur Uçar ◽  
Fatma Karakuş ◽  
Yusuf Yaylı
Keyword(s):  
Euclidean Space ◽  
Frenet Frame ◽  
Rotating Frame ◽  
Planar Curves ◽  
Bishop Frame ◽  
Darboux Frame ◽  
Rotating Frames

In this paper, generalized Fermi–Walker derivative, generalized Fermi–Walker parallelism and generalized non-rotating frame concepts are given for Frenet frame, Darboux frame and Bishop frame for any curve in Euclidean space. Being generalized, non-rotating frame conditions are analyzed for each frames along the curve. Then we show that Frenet and Darboux frames are generalized non-rotating frames along all curves and also Bishop frame is generalized non-rotating frame along planar curves in Euclidean space.

ON THE FERMI–WALKER DERIVATIVE AND NON-ROTATING FRAME

2012 ◽  
Vol 09 (08) ◽  
pp. 1250066 ◽  
Author(s):  
FATMA KARAKUŞ ◽  
YUSUF YAYLI
Keyword(s):  
Plane Curves ◽  
Frenet Frame ◽  
Rotating Frame ◽  
Bishop Frame ◽  
Darboux Frame ◽  
Line Of Curvature

In this study Fermi–Walker derivative and according to the derivative Fermi–Walker parallelism and non-rotating frame concepts are given for some frames. First, we get the Frenet frame, the Darboux frame, the Bishop frame for any curve in Euclid space. Fermi–Walker derivative and non-rotating frame being conditions are analyzed for each of the frames along the curve. Then we proved the Frenet frame is non-rotating frame along the plane curves. Darboux frame which is a non-rotating frame along the line of curvature. Then we proved the Bishop frame is a non-rotating frame along the all curves.

scholarly journals A Note on Minimal Translation Graphs in Euclidean Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 889 ◽  
Author(s):  
Dan Yang ◽  
Jingjing Zhang ◽  
Yu Fu
Keyword(s):  
Euclidean Space ◽  
Translation Surfaces ◽  
Planar Curves

In this note, we give a characterization of a class of minimal translation graphs generated by planar curves. Precisely, we prove that a hypersurface that can be written as the sum of n planar curves is either a hyperplane or a cylinder on the generalized Scherk surface. This result can be considered as a generalization of the results on minimal translation hypersurfaces due to Dillen–Verstraelen–Zafindratafa in 1991 and minimal translation surfaces due to Liu–Yu in 2013.

scholarly journals A New Angular Measurement in Minkowski 3-Space

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 56 ◽  
Author(s):  
Jinhua Qian ◽  
Xueqian Tian ◽  
Jie Liu ◽  
Young Ho Kim
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Angular Measurement ◽  
Frenet Frame ◽  
Measuring Methods ◽  
Null Curve

In Lorentz–Minkowski space, the angles between any two non-null vectors have been defined in the sense of the angles in Euclidean space. In this work, the angles relating to lightlike vectors are characterized by the Frenet frame of a pseudo null curve and the angles between any two non-null vectors in Minkowski 3-space. Meanwhile, the explicit measuring methods are demonstrated through several examples.

Relation between Darboux and type-2 Bishop frames in Euclidean space

2016 ◽  
Vol 13 (07) ◽  
pp. 1650101 ◽  
Author(s):  
Amine Yilmaz ◽  
Emin Özyilmaz
Keyword(s):  
Euclidean Space ◽  
Transition Matrix ◽  
Geodesic Curvature ◽  
Spherical Image ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Spherical Images

In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

scholarly journals N-BISHOP DARBOUX VECTOR OF A TIMELIKE CURVE IN MINKOWSKI 3-SPACE

2020 ◽  
Vol 20 (3) ◽  
pp. 519-528
Author(s):  
HATICE KUSAK SAMANCI
Keyword(s):  
Differential Geometry ◽  
Minkowski Space ◽  
Timelike Curve ◽  
Rotation Vector ◽  
Effective Alternative ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Alternative Approach ◽  
Darboux Frame ◽  
First Time

It is known that a Bishop frame of a curve is one of the effective alternative approach in the differential geometry. Recently, several important works have been done about the Bishop frames. The aim of our paper is to investigate the N-Bishop frame for timelike curves in Minkowski space. We define the N-Bishop frame for the timelike curve in Minkowski space. Then, we consider some properties of the frame. Moreover, we describe the N-Bishop Darboux frame for the first time. Additionally, we compute some geometrical characterizations for the N-Bishop Darboux axis and momentum rotation vector.

scholarly journals Measuring Electromagnetic Fields in Rotating Frames of Reference

Universe ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 31
Author(s):  
Clive Speake ◽  
Antonello Ortolan
Keyword(s):  
Electromagnetic Fields ◽  
Reference Frames ◽  
Frame Of Reference ◽  
Rotating Frame ◽  
Coordinate Transformations ◽  
Rotating System ◽  
Spherical Shells ◽  
Physics Community ◽  
Rotating Frames ◽  
Rotating Reference Frames

We review the problem of transforming electromagnetic fields between inertial and rotating reference frames. We compare the method of straightforward tensor coordinate transformations adopted by Schiff in his well-known paper of 1939 with the method of Orthogonal Tetrads (OT) that was applied to this problem in 1964 by Irvine. Although both methods are mathematically rigorous, the transformed fields have different forms depending on the method adopted. We emphasize that the OT method is expected to predict the fields that would actually be measured by an observer in a rotating frame of reference. We briefly discuss existing experimental evidence that supports the OT approach, but point out that there appears to be little awareness in the physics community of this problem or its resolution. We use both methods to transform the electrostatic and magnetic fields generated by rotating charged spherical shells from an inertial into a co-rotating system. We also briefly describe how such an arrangement of shells could be used to measure rotation relative to the fixed stars.

Special relativity experiments explained from the perspective of the rotating frame

2019 ◽  
Vol 34 (31) ◽  
pp. 1950255
Author(s):  
A. Sfarti
Keyword(s):  
Special Relativity ◽  
Doppler Effect ◽  
Clock Synchronization ◽  
Length Measurement ◽  
Rotating Frame ◽  
Rotating Platform ◽  
New Approach ◽  
Rotor Experiment ◽  
Rotating Frames ◽  
The Doppler Effect

In this paper, we present an explanation of several fundamental tests of special relativity from the perspective of the frame co-moving with a rotating observer. The solution is of great interest for real-time applications because Earth-bound laboratories are inertial only in approximation. We present the derivation of the Sagnac, Michelson–Morley, Kennedy–Thorndike and the Hammar experiments as viewed from the Earth-bound uniformly rotating frame or, as in the case of the Mossbauer rotor experiments, from the perspective of the rotating device. An entire section is dedicated to length/time measurement and to clock synchronization and another one to the Doppler effect and aberration on uniformly rotating platforms. This paper brings new information in the following areas: – new approach for clock synchronization on a rotating platform – new approach for length measurement in rotating frames – new explanation of the Doppler effect and of the Mossbauer rotor experiment – new explanation of the Kennedy–Thorndike experiment. The main thrust of this paper is to give a consistent explanation of various tests of special relativity as judged from the perspective of the rotating frame of the experimental setup. In addition, we correct certain misconceptions relative to clock synchronization and length measurement that have survived a long time in the specialty literature. A special chapter is dedicated to the derivation of the Doppler effect and of aberration in rotating frames. It is shown that such derivation is far from being trivial.

NONLINEAR FREQUENCY SUPERPOSITION FOR ROTATING FRAMES

1996 ◽  
Vol 05 (03) ◽  
pp. 457-463
Author(s):  
BORIS V. GISIN
Keyword(s):  
Group Theory ◽  
Light Propagation ◽  
Nonlinear Frequency ◽  
Rotating Frame ◽  
Electrical Field ◽  
Linear Frequency ◽  
External Electrical Field ◽  
Netic Field ◽  
Optical Crystals ◽  
Rotating Frames

In the slowly varying magnitude approximation Maxwell’s equation describing light propagation in some electro-optical crystals under the action of an external electrical field, is equivalent to Pauli’s equation describing motion of particles with spin [Formula: see text] in a mag-netic field. Use of this analogy for measuring the deviation from the linear frequency superposition by transition to rotating frame is discussed. Some group theory aspects of nonlinear law are considered.

scholarly journals N-Bishop Darboux vector of the spacelike curve with spacelike binormal

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 353-360
Author(s):  
Hatice Kusak-Samanci ◽  
Huseyin Kocayigit
Keyword(s):  
Minkowski Space ◽  
Rotation Vector ◽  
Spacelike Curve ◽  
Geometrical Properties ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Darboux Frame ◽  
First Time

In this article, the N-Bishop frame in Minkowski space is investigated for spacelike curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.

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