We have seen how the earth rotates on its axis, and we have attributed the bulging of the earth at the equator to this influence.
"The Story of the Heavens" by Robert Stawell Ball
How is it that the axis of the earth is not perpendicular to the equator?
"A Philosophical Dictionary, Volume 2 (of 10)" by François-Marie Arouet (AKA Voltaire)
Similarly y = 0 is the equation of the axis of x.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
Hence, the axis of the earth is the axis of the equator, and its poles are the poles of the equator.
"Letters on Astronomy" by Denison Olmsted
Note that the y, z LT equations (2.3) and (2.4) ((E3.29) and (E3.30) in Einstein’s notation) together with the TD relation (6.1) predict, in accordance with Einstein’s assumption in deriving (E3.16) and (E3.17) that the apparent speed, in S, of light signals propagating perpendicular to the ξ axis in S’ is c.
The physics of space and time II: A reassessment of Einstein's 1905 special relativity paper
We can then have two situations: if the non-axisymmetric effect does not depend on the sense of the axis of symmetry (e.g. the Lorentz forces generated by the perturbed magnetic ﬁeld), then the problem is invariant und er reﬂection about the equator and some degeneracy remains.
Asteroseismic Theory of Rapidly Oscillating Ap Stars
In the extreme case where all the matter would be ejected along narrow jets centred on the rotational axis, nearly no angular momentum would be lost, while if all the matter is ejected near the equator plane, this maximizes the amount of angular momentum lost.
Evolution towards the critical limit and the origin of Be stars
N-soliton solutions and the solutions with rational axis data The N-soliton solutions for vacuum Einstein equations had been discovered by Belinski and Zakharov [10, 32] in the framework of their formulation of the inverse scattering method.
This concludes our outlines of the integral equation methods and their interrelations as well as of interrelations between the classes of soliton solutions and the solutions with arbitrary axis data and now we are ready to give less formal comments of some strange aspects of the paper of F.J.
Thus, these equations should not be identiﬁed with or represented as a combination of the Hauser - Ernst - Sibgatullin equations, though they describe the same space of stationary axisymmetric electrovacuum solutions with a regular axis of symmetry.
The ﬁelds satisfy Maxwell’s equations on the complement of the z axis.
Incoming and disappearing solutions for Maxwell's equations
As show results of numerical integration of equations of motion with taking into account of true jet forces, acting on a star, the use of Paczynski-Huang model results in signiﬁcant mistakes in deﬁnition of the semi-ma jor axis, down to an opposite sign of derivative ˙a.
Elliptical motions of stars in close binary systems
While the process is easier and faster than normal off-axis source calibration or peeling, in practice it will be of little use: it neglects information present in polarizations, as deﬁned by the measurement equation (Hamaker et al. 1996), and neglects the relations between baselines.
Post-correlation filtering techniques for off-axis source and RFI removal
In the ﬁrst equation, a,e are the semi-ma jor axis and the eccentricity of the perturded planet and GM⊙ is the mass of the sun.
Planetary ephemerides and gravity tests in the solar system
A simple rescaling of the z -axis transforms the above expression into the Poisson equation.
Real-space cosmic fields from redshift-space distributions: a Green function approach
To make the radial conﬁnement 10 times stronger than this axial conﬁnement we require an alternating voltage on the radial quadrupole electrodes of frequency ΩV ≃ 2π × 1.2 MHz (equation (31)) and amplitude V ≃ 9 volts (equation (30)), assuming a distance of ∼ 1 mm from the axis to the radial electrode surfaces.
The Ion Trap Quantum Information Processor
Recall that the appearance of the axis of time, in standard general relativity, is a consequence of specifying an initial and a ﬁnal 3-geometry on two spacelike hypersurfaces plus evolution according to the ﬁeld equation .
Are We Cruising a Hypothesis Space?
We now rotate this solution, with the symmetry axis of the wave rotated into the equator, to generate a non-axisymmetric solution.
Test Evolution of Non-Axisymmetric Gravitational Waves
It turns out that this equation is diﬃcult to solve for points off the axis of symmetry, but the solution can be found for points on the axis of symmetry.
Radiation from SU(3) monopole scattering