Nonrotating reference frames for the Gödel and Kerr metrics

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040048
Author(s):  
R. X. Saibatalov

The coordinate transformations are proposed to transform Gödel and Kerr metrics to a nonrotating form by the uniform way.

Universe ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 31
Author(s):  
Clive Speake ◽  
Antonello Ortolan

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.


2021 ◽  
Vol 21 (2) ◽  
pp. 166-179
Author(s):  
A.I. Gudimenko ◽  

The theory of hydrodynamic reduction of non-autonomous Hamiltonian mechanics (V. Kozlov, 1983) is presented in the geometric formalism of bundles over the time axis R. In this formalism, time is one of the coordinates, not a parameter; the connections describe reference frames and velocity fields of mechanical systems. The equations of the theory are presented in a form that is invariant with respect to time-dependent coordinate transformations and the choice of reference frames.


Author(s):  
David D. Nolte

This chapter emphasizes the importance of a geometric approach to dynamics. The central objects of interest are trajectories of a dynamical system through multidimensional spaces composed of generalized coordinates. Trajectories through configuration space are parameterized by the path length element, which becomes an important feature in later chapters on relativity and metric spaces. Trajectories through state space are defined by mathematical flow equations whose flow fields and flow lines become the chief visualization tool for complex dynamics. Coordinate transformations and Jacobian matrices are used throughout this text, and the transformation to noninertial frames introduces fictitious forces like the Coriolis force that are experienced by observers in noninertial frames. Uniformly rotating frames provide the noninertial reference frames for the description of rigid-body motion.


2000 ◽  
Vol 12 (12) ◽  
pp. 2823-2855 ◽  
Author(s):  
J. McIntyre ◽  
F. Stratta ◽  
J. Droulez ◽  
F. Lacquaniti

The execution of a simple pointing task invokes a chain of processing that includes visual acquisition of the target, coordination of multimodal proprioceptive signals, and ultimately the generation of a motor command that will drive the finger to the desired target location. These processes in the sensorimotor chain can be described in terms of internal representations of the target or limb positions and coordinate transformations between different internal reference frames. In this article we first describe how different types of error analysis can be used to identify properties of the internal representations and coordinate transformations within the central nervous system. We then describe a series of experiments in which subjects pointed to remembered 3D visual targets under two lighting conditions (dim light and total darkness) and after two different memory delays (0.5 and 5.0 s) and report results in terms of variable error, constant error, and local distortion. Finally, we present a set of simulations to help explain the patterns of errors produced in this pointing task. These analyses and experiments provide insight into the structure of the underlying sensorimotor processes employed by the central nervous system.


2004 ◽  
Vol 92 (4) ◽  
pp. 2622-2627 ◽  
Author(s):  
Ryan R. Metzger ◽  
O'Dhaniel A. Mullette-Gillman ◽  
Abigail M. Underhill ◽  
Yale E. Cohen ◽  
Jennifer M. Groh

Auditory spatial information arises in a head-centered coordinate frame, whereas the saccade command signals generated by the superior colliculus (SC) are thought to specify target locations in an eye-centered frame. However, auditory activity in the SC appears to be neither head- nor eye-centered but in a reference frame that is intermediate between both of these reference frames. This neurophysiological finding suggests that auditory saccades might not fully compensate for changes in initial eye position. Here, we investigated whether the accuracy of saccades to sounds is affected by initial eye position in rhesus monkeys. We found that, on average, a 12° horizontal shift in initial eye position produced only a 0.6 to 1.6° horizontal shift in the endpoints of auditory saccades made to targets at a range of locations along the horizontal meridian. This shift was similar in size to the modest influence of eye position on visual saccades. This virtually complete compensation for initial eye position implies that auditory activity in the SC is read out in a manner that is appropriate for generating accurate saccades to sounds.


2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Emre Dil ◽  
Talha Zafer

We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of f(R) gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.


2001 ◽  
Author(s):  
Joseph S. Lappin ◽  
Duje Tadin ◽  
Emily Grossman

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