Spinning Object Research Articles

Spin and Translation, the Equation of Motion

The effect of spin on the equation of motion of a sliding object is assessed. The spatial dependence of the friction force on a spinning object is calculated and used to describe the equation of motion.

A Simple Method to Measure the Angular Speed of a Spinning Object

The angular speed of a spinning object is commonly measured using a stroboscope or a mechanically or optically coupled tachometer. We present here an alternate, simple, and instructive method to measure it using a microphone and a computer.

GRAVITATIONAL WAVEFORMS FOR FINITE MASS BINARIES

One of the promising sources of gravitational radiation is a binary system composed of compact stars. It is an important question of how the rotation of the bodies and the eccentricity of the orbit affect the detectable signal. Here we present a method to evaluate the gravitational wave polarization states for inspiralling compact binaries with comparable mass. We consider eccentric orbits and the spin-orbit contribution in the case of one spinning object up to 1.5 post-Newtonian order. For circular orbits our results are in agreement with existing calculations.

Motion in Kaluza-Klein type theories

Path and path deviation equations for charged, spinning and spinning charged objects in different versions of Kaluza-Klein (KK) theory using a modified Bazanski Lagrangian have been derived. The significance of motion in five dimensions, especially for a charged spinning object, has been examined. We have also extended the modified Bazanski approach to derive the path and path deviation equations of a test particle in a version of non-symmetric KK theory.

Pulsar Sets a Dizzying Standard

AMERICAN ASTRONOMICAL SOCIETY MEETINGWASHINGTON, D.C.-- Astronomers have found the fastest spinning object in space. The work was reported at the American Astronomical Society meeting here on 8 to 12 January and in the 12 January online edition of Science ([www.sciencemag.org/cgi/content/abstract/1123430][1]). ([Read more][2].) Other briefs from the meeting: [Laser Points to Bright New Era for Ground-Based Astronomy][3] [Pesky Companions Warp the Milky Way][4] [Snapshots From the Meeting][5] [1]: http://www.sciencemag.org/cgi/content/abstract/1123430 [2]: http://www.sciencemag.org/cgi/content/full/311/5761/602b [3]: http://www.sciencemag.org/cgi/content/short/311/5761/602a [4]: http://www.sciencemag.org/cgi/content/short/311/5761/603a [5]: http://www.sciencemag.org/cgi/content/short/311/5761/603b

Dynamic aggregation of chiral spinners.

An object spinning at the surface of a liquid creates a chiral vortex. If the spinning object is itself chiral, its shape modifies the characteristics of the vortex; interactions between that vortex and other vortices then depend on the chirality of the objects that produce them. This paper describes the aggregation of millimeter-sized, chiral magnetized plates floating at a liquid-air interface and rotating under the influence of a rotating external magnetic field. This external field confines all the plates at densities that cause the vortices they generate to interact strongly. For one set of plates investigated, plates of one chirality attract one another, and plates of the other chirality repel other plates of both chiralities.

Epipolar geometry from profiles under circular motion

Addresses the problem of motion estimation from profiles (apparent contours) of an object rotating on a turntable in front of a single camera. A practical and accurate technique for solving this problem from profiles alone is developed. It is precise enough to reconstruct the shape of the object. No correspondences between points or lines are necessary. Symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly. These, together with geometric constraints for images of rotating objects, are used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar geometry of the image sequence. The estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms. The search for the epipoles, by far the most critical step, is carried out as a simple 1D optimization. Parameter initialization is trivial and completely automatic at all stages. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self-calibration techniques. Finally, the spinning object is reconstructed from its profiles using the motion estimated in the previous stage. Results from real data are presented, demonstrating the efficiency and usefulness of the proposed methods.

Centrifuge polarizing microscope. I. Rationale, design and instrument performance

We first describe early uses of the centrifuge for deciphering physical properties and molecular organization within living cells, as well as the development and use of centrifuge microscopes for such studies. The rationale for developing a centrifuge microscope that allows high-extinction polarized light microscopy to observe dynamic fine structures in living cells is next discussed. We then describe a centrifuge polarizing microscope (CPM) that we developed for observing fine structural changes in living cells which are being exposed to up to approximately 11 500 times earth's gravitational field (g). With the specimen housed in a rotor supported on an air spindle motor, and imaged through an external microscope illuminated by a precisely synchronized flash of less than 10 ns duration from a Nd:YAG laser, the image of the spinning object remains steady up to the maximum speed of 11 700 rev min-1, or up to approximately 11 500 x g. The image is captured, at up to 25 frames s-1, by an interference-fringe-free CCD camera that is synchronized to the centrifuge rotor. At all speeds (in 100 rev min-1 increments), the image is resolved to better than 1 microm, while birefringence of the specimen, housed in a specially designed specimen chamber that suffers low-stress birefringence and prevents leakage of the physiological solutions, is detected with a retardance sensitivity of better than 1 nm. Differential interference contrast and fluorescence images (532 nm excitation) of the spinning specimen can also be generated with the CPM. The second part of this study (Inoué et al., J. Microsc. 201 (2001) 357-367, describes several biological applications of the CPM that we have explored. Individual live cells, such as oocytes and blood cells, are supported on a sucrose or Percoll density gradient while other cells, such as cultured fibroblasts and Dictyostelium amoebae, are observed crawling on glass surfaces. Observations of these cells exposed to the high G fields (centripetal acceleration/g) in the CPM are yielding many new results that lead to intriguing questions regarding the organization and function of fine structures in living cells and related quasi-fluid systems.

The motion of a spinning object in a higher-dimensional spacetime

We solve exactly the equations of 5D general relativity for the case of a spinning test object moving in a circular orbit in a Schwarzschild-like spacetime augmented by one extra dimension. All of the classical tests give their standard results, but the spin axis precesses at a different rate in 4D and 5D. This suggests that the dimensionality of the world could be tested using a gyroscope in Earth orbit.

Integration of classical and quantum physics.

The perennial aspect of the Newtonian foundation of mathematical physics is that the concept of motion,'' that is, kinematics,'' is to serve as the interface between mathematics and physics. Kinematics subdivides into the theory of orbital translation and that of undulation and spinning. Newtonian mechanics is based on giving to translational kinematics a priority over the other modes, since planetary revolution can be represented as translation modified by gravitation. The so-called breakdown of classical physics stems from giving the translational priority a canonical status and extending it to the constituents of matter. We claim that in this case the priority is to be reversed. The main content of this paper is to establish the algebraic model for an indivisible, undulating entity that we call a wave simplex.'' It is used as the point of departure for a non-Newtonian quantum dynamics in which physical and algebraic concepts are in close correspondence. The postulates of the classical phenomenological theories and those of the canonical theories based on translational priority are established as theorems under the proper limiting conditions, and forces are constructed rather than postulated. While the formal structure of two-level quantum mechanics is established as well, exception is taken to treatingmore » spin as a property of a point particle. It is considered self-evident that a spinning object is orientable, a property accounted for in terms of a unitary triplet. This is the point of departure for an intrinsic particle dynamics. A main result is the integration of classical and quantum physics, thus closing the gap created by the heuristic method of canonical quantization.« less

Is Geminga a very close neutron star binary?

Geminga (2CG195+4) is one of the brightest sources in the sky at photon energies around 1 GeV (refs 1–3). It has been tentatively identified4 with an unusual soft X-ray and optical object for which the γ-ray-to-X-ray-to-optical luminosity ratios are ∼106:103:1, which may now have been confirmed by the discovery5 of a ∼60-s periodic variation in the X-ray source, similar to that reported in γ rays. The period has been increasing over the past 10 yr at a rate such that it doubles in ∼400–800 yr. The implied rotational energy loss would supply the γ-ray luminosity of Geminga if the spinning object were a neutron star at a distance of ∼10 pc, consistent with the very low observed X-ray absorption. A lone pulsar with a spin period of ∼60 s cannot spin down at the required rate. The observed period would need to be due to precession or some other process. We show here that the presence of a close neutron star companion provides a suitable mechanism. All neutron star binaries may evolve through a Geminga-like phase.

The Application of Tomimatsu-Sato Metric to the Gravitational Field of Ordinary Spinning Object

An expression of the Tomimatsu-Sato metric in the Schwarzschild coordinates is found. In it those small terms of are omitted. The resulting expression is applied to the description of gravitational field of ordinary spinning objects such as the sun. The Landau-Lifshitz method used to find the deflection of light and precession of perihelia in the Schwarzschild field is generalized to the gravitational field of a spinning object. It is shown that the expressions of the deflection of light and precession of perihelia in the Tomimatsu-Sato field are the same as those in the Kerr field. Tomimatsu and Sato have conjectured that their metric is more appropriate for describing the gravitational field of ordinary spinning object than Kerr metric. In order to check this conjecture one must consider the terms smaller than .

Compact variable extragalactic objects and small-pitch-angle synchrotron theory

A small-pitch-angle synchrotron radiation model of luminous compact variable radio sources is applied to a large class of such objects. The model consists of a massive spinning object endowed with an extended magnetosphere. The electrons are accelerated near its surface by a strong electric field, spiral along the field lines, and lose their energy by the small-pitch-angle synchrotron process responsible for the observed centimeter and infrared radiation. The model adequately explains the observed variability of the majority of compact sources for (rest frame) frequencies greater about 10 GHz. The model is not able to account for the variability of sources at lower frequencies, indicating clearly that an investigation alternative radiation mechanisms or relativistic effects resulting from bulk motion is necessary.

Balancing of Electromagnetic and Gravitational Forces and Torques Between Spinning Particles at Rest

The results reported here arise from a line of development that includes the following: (1) Schiff (1960), precession of a spinning object in a gravitational field endowed with "magnetic" components, (2) Oliveira and Tiomno (1962), same precession derived from the Dirac equation plus correspondence principle, (3) present work, determination of the force on a spinning object again by use of Dirac's equation plus the correspondence principle - in agreement with what Wald and what Wilkins and Ruffini find from Papapetrou's classical equations of motion for a spinning object. The same result also follows from Kramer's classical nonrelativistic Hamiltonian formalism applied to electromagnetic and gravitational interactions. We demand that any coupling of a spinning object with a "magnetic" type of gravitational field must satisfy the principle of equivalence of gravitational and inertial forces in the sense that the gravitational "gyromagnetic" factor must be exactly unity. The resulting equations of motion are used to prove that if a system of arbitrarily spinning charged particles, satisfying the conditions ${q}_{i}={m}_{i}$ and with gyromagnetic factors ${g}_{i}=2$, is initially at rest it will remain at rest and without precession of the spins. This gives an insight on how the solutions of the Einstein-Maxwell equations recently obtained by Perj\'es and by Israel and Wilson can be stationary in spite of a nonvanishing magnetic field.

Optimal inner-product angular momentum controllers

An optimization technique is presented to reduce to zero the angular velocities of a spinning object while minimizing a general performance criterion. Closed-form control laws are obtained for a controller structure with a single nonlinear transducer in the feedback loop that employs the square of the Euclidean distance to the origin as an error signal. Consideration is also given to the inverse problem of optimal control. Linearization and generalization of the nonlinear plant are discussed.