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Showing papers on "Rotation published in 1981"


Journal ArticleDOI
TL;DR: In this article, the periodic variations of the earth's rotation resulting from the tidal deformation by the sun and moon were rederived including terms with amplitudes of 0.002 millisecond and greater.
Abstract: The periodic variations of the earths' rotation resulting from the tidal deformation of the earth by the sun and moon were rederived including terms with amplitudes of 0.002 millisec and greater. The series applies to the mantle, crust, and oceans which rotate together for characteristic tidal periods; the scaling parameter is the ratio of the fraction of the Love number producing tidal variations in the moment of inertia of the coupled mantle and oceans (k) to the dimensionless polar moment of inertia of the coupled moments (C). The lunar laser ranging data shows that k/C at monthly and fortnightly frequencies equals 0.99 + or - 0.15 and 0.99 + or - 0.20 as compared to the theoretical value of 0.94 + or - 0.04.

267 citations



Journal ArticleDOI
TL;DR: In this article, a simulated horizon visual display was used to investigate whether the ocelli may function synergistically with the compound eyes to minimize the delay of visual responses and augment visual responses when no sharp horizontal border is present.
Abstract: Locusts (Orthoptera, Acrididae) were tethered inside a simulated horizon visual display. Rotation of the horizon elicited following motions of the animal's head and rudderlike movements during flight. Head and steering motions were still elicited after either the compound eyes or the ocelli were surgically ablated. Head motions after ocellar cautery suggested that the ocelli may function synergistically with the compound eyes to (a) minimize the delay of visual responses and (b) augment visual responses when no sharp horizontal border is present. Flight steering motions were found not to depend on proprioception of head position. Three other species (Diptera and Odonata) also followed horizon rotations with head motion after their compound eyes had been ablated.

191 citations


Journal ArticleDOI
TL;DR: The perception of the apparent frequency of rotation of gratings of various spatial-frequencies and contrast is investigated and high spatial-frequency and low contrast gratings appear to move slower and an oscilloscope spot oscillating back and forth at a constant velocity appears to have a lower velocity in the peripheral field.

131 citations


Journal ArticleDOI
01 Oct 1981-Nature
TL;DR: In this article, a measurement of the splitting of the discrete lines in the 5-min oscillations of the solar surface produced experimental evidence for the rapid internal rotation of the Sun, and the number of components into which the lines are split also allows unambiguous identification of 11 examples of each of the l = 0, l = 1 and l = 2 modes in the frequency range 2.40-3.85 mHz.
Abstract: The observation of line-of-sight velocities of the solar surface by means of Doppler shift measurements of the Fraunhofer absorption lines, using optical resonance scattering, has proved a useful technique in solar physics enabling the discovery of long period solar oscillation1, the discrete, regular structure in the 5-min oscillation2 and, as we report here the splitting of this structure by rotational effects. A measurement of the splitting of the discrete lines in the 5-min oscillations of the solar surface produced experimental evidence for the rapid internal rotation of the Sun. These data demonstrate that the Sun does not rotate uniformly but that the ‘core’ of the Sun rotates 2–9 times as rapidly as the observed surface rotation. The number of components into which the lines are split also allows unambiguous identification of 11 examples of each of the l = 0, l = 1 and l = 2 modes in the frequency range 2.40–3.85 mHz.

116 citations


Journal ArticleDOI
TL;DR: In this paper, Doppler shifts of appropriate spectra lines were made from both hydrogen and deuterium beams and include data from both co-and counter-injection at several electron densities.
Abstract: Toroidal plasma rotation in the Princeton Large Torus, PLT, has been measured for various plasma and neutral-beam injection conditions. Measurements of the plasma rotational velocities were made from Doppler shifts of appropriate spectra lines and include data from both hydrogen and deuterium beams and co- and counter-injection at several electron densities. Without injection, a small but consistent toroidal rotation exists in a direction opposite to the plasma current (counter-direction) in the plasma centre but parallel to the current (co-direction) in the plasma periphery. Using these velocities measured in the absence of injection, and the plasma density and temperature gradients, radial electron fields can be determined from theory, giving Er ≈ 40 V · cm−1 in the plasma centre and Er ≈ 10 V · cm−1 near the plasma edge. Insertion of a local, 2.5% magnetic well produced no observable effect on the beam-driven rotation. Modelling of the time evolution and radial distribution of the rotation allows one to deduce an effective momentum diffusivity of the order of (1–5) × 104 cm2 · s−1.

105 citations


Journal ArticleDOI
01 Aug 1981
TL;DR: In this article, a semianalytic libration theory is proposed for analyzing observations of the Moon, where the Moon is assumed to be either rigid, elastic or anelastic, and its gravity potential is represented through its fourth degree harmonics.
Abstract: In 1693, Jean Dominique Cassini disclosed his finding that the rotational motion of the Moon could be neatly described by the superposition of two uniform motions, a prograde rotation of the Moon about its polar axis and a retrograde precession of the Moon's equator along the ecliptic. The description of these motions is now called Cassini's laws. The theoretical explanation of Cassini's laws shows that physical librations with amplitudes less than 0″.5, as seen from the Earth, must also exist. Until 1970, the physical librations were just marginally discernible, and the dynamical theory was developed to a level far superior to the quality of the observations. In 1970 the resolution of libration observations jumped by a factor of 104 over earlier techniques, and existing theories became inadequate for analyzing the observations. This paper presents a new semianalytic libration theory that is of use for analyzing observations. In this development the Moon is assumed to be either rigid, elastic or anelastic, and its gravity potential is represented through its fourth-degree harmonics. The Moon is considered to be moving about the Earth in an orbit that is perturbed by the Sun (the ALE of Deprit, Henrard and Rom), and by the planets and the figures of the Earth and Moon (from the ILE, principally derived by Brown). The direct effects of the rotation of the plane of the ecliptic and the figure of the Earth are also considered. Tables for physical libration variables are tabulated which are truncated at 0″.010.

93 citations


Journal ArticleDOI
TL;DR: In this paper, the inner core is modeled by two solid spheres permeated by a uniform field of 5 Gauss representing the dipole, and the inner sphere is free to rotate relative to the outer sphere.
Abstract: We cannot observe the magnetic field inside the earth's core directly, but there is likely to be a large toroidal part of 10–100 Gauss which, together with the dipole component, could produce a magnetic torque on the inner core that tends to rotate it. Estimates based on dynamo calculations give torques of 1019 N m which is large enough to accelerate the inner core to the westward drift velocity of 0.2° per year within a few days. Presumably some equilibrium has been reached in which the inner core rotates with constant angular velocity and experiences no net torque. This rotation should have significant consequences for dynamo calculations because it is a very effective method of stretching field lines, and its helps to drive differential rotation in the liquid outer core. The core is modeled by two solid spheres permeated by a uniform field of 5 Gauss representing the dipole. The inner sphere is free to rotate relative to the outer sphere. When a torque of 1019 N m is applied to the inner sphere it reaches equilibrium with a steady angular velocity corresponding to a rotation period of 2300 years, which is similar to the westward drift speed, and a toroidal field of about 100 Gauss is induced. The inner sphere can also undergo toroidal oscillations with a period of about 10 years which may be related to the observed secular variation.

92 citations


Patent
07 Jan 1981
TL;DR: In this article, a gyro-wave energy transducer is mounted on a buoyant body for translating pendulum-like motions of the body into rotational motion, and a motor/generator is coupled to the gyroscope for maintaining a controlled rotational velocity.
Abstract: A mechanism for generating power from wave motion on a body of water. The mechanism includes a buoyant body which is adapted to float on a body of water and to roll and pitch in response to the wave motion of the water. A gyro-wave energy transducer is mounted on the buoyant body for translating the pendulum-like motions of the buoyant body into rotational motion. The gyro-wave energy transducer includes a gimbal comprised of first and second frames, with the first frame being pivotally mounted to the second frame and the second frame being pivotally mounted to the buoyant body. A gyroscope is mounted to the first frame for rotation about an axis perpendicular to the axes of rotation of the first and second frames. A motor/generator is coupled to the gyroscope for maintaining a controlled rotational velocity for the gyroscope. Transferring members are associated with one of the first and second frames for transferring torque of one of the first and second frames to the gyroscope about an axis that is perpendicular to that of the gyroscope which results in rotation of the other of the first and second frames. An electrical generator is responsive to the relative rotational movement of the first and second frames for generating electrical energy. A storage battery is mounted on the buoyant body for storing and releasing electrical energy and is operatively coupled to the motor/generator and the electrical generator. A control circuit is associated with the generator and the motor/generator unit of the gyroscope and is responsive to the time rate of change of current produced by the generator for controlling the rotational velocity of the gyroscope in order to maintain maximum power output from the electrical generator.

87 citations


Journal ArticleDOI
01 Jan 1981

87 citations


Journal ArticleDOI
TL;DR: A major source of noise in fiber-optic Sagnac interferometers was identified to be the fluctuation of the phase of Rayleigh backscattering resulting from minute temperature variations and vibration.
Abstract: A major source of noise in fiber-optic Sagnac interferometers was identified to be the fluctuation of the phase of Rayleigh backscattering resulting from minute temperature variations and vibration. This noise can be reduced either by introducing a phase modulation into the fiber ring or by the use of a low-coherence source. A noise-equivalent rotation rate of 8 x 10(-4) deg/sec was achieved.

Patent
13 Jul 1981
TL;DR: In this paper, a technique for converting solar energy directly to electrical energy is presented, which utilizes a plurality of photovoltaic-like flat panels having solar collecting front sides.
Abstract: A technique for converting solar energy directly to electrical energy is disclosed herein and utilizes a plurality of photovoltaic-like flat panels having solar collecting front sides. These panels are supported for simultaneous rotation about a given axis, preferably a horizontal or south sloping axis, while their solar collecting front sides face the same direction. At the same time, these front sides are maintained in end-to-end relationship with one another within a common plane, preferably one which is at all times parallel with the axis of rotation. In actual operation, the photovoltaic-like panels are simultaneously rotated about their given axis in tracking relationship with the sun, preferably so as to maintain the solar collecting front sides of the panels at a fixed acute angle with respect to the sun's rays. Moreover,the panels are preferably supported adjacent to one another in a way which minimizes the distance between endmost panels.

Journal ArticleDOI
TL;DR: Evidence that early eye rotation in Xenopus leads to anatomical rearrangements in a portion of the binocular visual system is presented and results demonstrate that the orientation of a topographically organized projection can be changed by procedures which do not involve direct manipulation of the source, pathway, or target of the projection.
Abstract: In this paper we present evidence that early eye rotation in Xenopus leads to anatomical rearrangements in a portion of the binocular visual system. In the past, electrophysiological mapping had shown that the topography of the ipsilateral visuotectal projection is changed by such eye rotation and that this change requires visual experience. However, knowledge of the anatomical basis for this electrophysiological change was lacking. The identification of the nucleus isthmi as a link in the projection has allowed us to study the topography of the ipsilateral system by use of horseradish peroxidase. We present data showing that early eye rotation alters the topography of the crossed isthmotectal projection. These results demonstrate that the orientation of a topographically organized projection can be changed by procedures which do not involve direct manipulation of the source, pathway, or target of the projection.

Journal ArticleDOI
TL;DR: In this article, the rotational and translational motions of single diatomic molecules in the liquid state are investigated for both the homo- and heteronuclear cases using computer simulations using the method of molecular dynamics.
Abstract: The coupling between the translational and rotational motions of single diatomic molecules in the liquid state is investigated for both the homo- and heteronuclear cases. ‘Experimental’ data are provided by computer simulations using the method of molecular dynamics. Their analysis is made in terms of low order time correlation functions of the translational velocity V of the centre of mass and the rotational velocity ω; these correlation functions are defined in two different ways: (a) with respect to the fixed laboratory axis and (b) with respect to a moving reference frame attached to the molecule itself. It is observed, at the level of the correlation matrix {V, ω}, that the rotation-translation coupling appears only indirectly in presentation (a) while direct evidence is provided in presentation (b). Further, this second presentation displays qualitative differences between homo- and heteronuclear molecules. These results should help in clarifying the validity of various stochastic equations modellin...

Patent
27 Apr 1981
TL;DR: In this article, an improved apparatus for effecting the cementing of a liner at the bottom of a well bore is described, where the liner sleeve assembly is inserted into the well bore on a hanger which is detachably connected to a running tool, which, in turn, is connected to the work string by a torque transmitting expansion joint.
Abstract: The disclosure relates to an improved apparatus for effecting the cementing of a liner at the bottom of a well bore. The liner sleeve assembly is inserted into the well bore on a hanger which is detachably connected to a running tool, which, in turn is connected to the work string by a torque transmitting expansion joint. The running tool may be fluid pressure actuated to set the hanger. In the event of failure of the fluid pressure setting operation, the hanger may be mechanically set by rotation of the work string transmitted to the running tool by the torque transmitting expansion joint.

Journal ArticleDOI
Mario Liu1
TL;DR: In this article, a nonlinear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary.
Abstract: Biaxial nematics are usually regarded as characterized by a symmetric, traceless tensor having three different eigenvalues. It is argued that this definition is too restrictive and that a natural extension would embrace any system that breaks all three rotational symmetries while preserving translational invariance. That is, biaxial nematics need not have orthorhombic symmetry, but may be triclinic, hexagonal, cubic, or even isotropic. A non-linear hydrodynamic theory is presented which emphasizes the fundamental similarities between the different biaxial nematics and clarifies the changes in the static and dynamic behavior as the discrete symmetries vary. The Goldstone modes of any biaxial nematics are identified as two pairs of orbital waves with a complex, and one orbital diffusion with a purely imaginary, dispersion relation. If the longitudinal and transverse variables decouple, it is the longitudinal rotation angle that diffuses.

Journal ArticleDOI
TL;DR: In this paper, the fundamental frequency coefficient for a rectangular plate with edges elastically restrained against both translation and rotation is calculated by using polynomial coordinate functions and the Rayleigh-Ritz method.

Patent
26 May 1981
TL;DR: In this paper, a turbine for utilization of the kinetic energy of moving air or fluid is described, which is comprised of a rotor mounted for rotation about a central axis (21) with respect to a support member (22) and connected to means (23) for converting rotation of the rotor (20) to usable energy.
Abstract: A turbine apparatus for utilization of the kinetic energy of moving air or fluid is disclosed. The turbine apparatus is comprised of a rotor (20) mounted for rotation about a central axis (21) with respect to a support member (22) and connected to means (23) for converting rotation of the rotor (20) to usable energy. The rotor (20) includes a plurality of blades (40, 41, 42) disposed symmetrically about the central axis (21), each of the blades having an outer edge (43) and an inner edge (44) with respect to the central axis (21). In addition, each blade (40, 41, 42) has a curved portion (45) and a second portion (46), the curved portion (45) beginning at the outer edge (43) and terminating at the second portion (46). The curved portion (45) has a surface generally concave with respect to the central axis (21). The second portion (46) extends from the curved portion (45) and terminates at the inner edge (44). The inner edge lies in a plane containing the central axis, the plane being disposed at an angle greater than 60° measured about the central axis (21) from a plane containing the outer edge (43) and the central axis (21). Variations of these and other components of the present invention are also described.

Journal ArticleDOI
01 Apr 1981-Nature
TL;DR: In this article, the correlation between Earth rotation and magnetic field variations has been clarified by studying those magnetic field indicators that are the most sensitive to variations in westward drift of the outer regions of the core.
Abstract: Numerous studies of the variations of the Earth's rotation have been made since 1900 (summarized in refs 1, 2). It seems well established that variations in the rotation with periods equal to or less than 2 yr are due to variations in the zonal circulation of the atmosphere2–4. However, there is no general agreement about the cause of the longer-period variations of the Earth's rotation, sometimes known as the ‘decade variations’, although the most favoured explanation is electromagnetic core–mantle coupling (see ref. 5). Several studies6–8 of the correlation between Earth rotation and magnetic field variations have obtained marginally positive results. We have been able to clarify such a correlation over the past 120 yr by studying those magnetic field indicators that are the most sensitive to variations in westward drift of the outer regions of the core. We suggest here that the correlation can be extended back ∼300 yr. Simple models of core–mantle coupling, based on Dullard's ideas, give reasonable quantitative agreement with the observations.

Patent
07 Oct 1981
TL;DR: In this article, an improved compact optical gyro is provided wherein a beam of light is split and introduced into both ends of an optic coil whose rotation is to be sensed, at least one frequency shifter is placed to affect the frequency of the beam to introduce or adjust a non-reciprocal phase shift.
Abstract: An improved compact optical gyro is provided wherein a beam of light is split and introduced into both ends of an optic coil whose rotation is to be sensed. At least one frequency shifter is placed to affect the frequency of the beam to introduce or adjust a nonreciprocal phase shift. The beams are then mixed back together and the resultant beam is detected and analyzed by suitable circuitry to provide an output indicative of the rotation of the light path.

Patent
Takeo Hiramatsu1
27 May 1981
TL;DR: In this article, a torque transmission device for eliminating the transmission of tortional vibration from a driving shaft to a driven shaft comprises a clutch capable of controlled slippage so that the speed of rotation of the driven shaft is lower than speed of the driving shaft.
Abstract: A torque transmission device for eliminating the transmission of tortional vibration from a driving shaft to a driven shaft comprises a clutch capable of controlled slippage so that the speed of rotation of the driven shaft is lower than the speed of the driving shaft. Slippage of the clutch is controlled by sensing the speed of rotation and the fluctuation of the speed of rotating of the driving shaft and the speed of rotation of the driven shaft and regulating slippage so that the difference in rotation speed between the two shafts is greater than the fluctuation in rotation speed of the driving shaft. The clutch may be an electromagnetic clutch of which the exciting current is controlled or a friction clutch actuated by controlled hydraulic pressure. The clutch may be in parallel with a fluid coupling.


Journal ArticleDOI
TL;DR: In this paper, the authors examined possible sources of systematic error in solar Doppler rotational velocities, including interference fringes at the spectrograph focus at Mount Wilson and the misalignment between the entrance and exit slits.
Abstract: Possible sources of systematic error in solar Doppler rotational velocities are examined. Scattered light is shown to affect the Mount Wilson solar rotation results, but this effect is not enough to bring the spectroscopic results in coincidence with the sunspot rotation. Interference fringes at the spectrograph focus at Mount Wilson have in two intervals affected the rotation results. It has been possible to correlate this error with temperature and thus correct for it. A misalignment between the entrance and exit slits is a possible source of error, but for the Mount Wilson slit configuration the amplitude of this effect is negligibly small. Rapid scanning of the solar image also produces no measurable effect.

Patent
27 Mar 1981
TL;DR: In this article, two concave spherical metal mirrors are used to scan a continuous wave laser beam for heat treating of metals, rotated in opposite directions and each is tilted at a small angle with respect to its axis of rotation.
Abstract: Two concave spherical metal mirrors are used to scan a continuous wave laser beam for heat treating of metals. The mirrors are rotated in opposite directions and each is tilted at a small angle with respect to its axis of rotation. The frequencies of rotation of the mirrors are made constant by a precision timing drive linkage which also allows for phase adjustment. The beam deflection from an individual mirror describes an ellipse, but the deflection when added to that from the second mirror with the proper phase relationship to the first is a straight line. The input laser beam, which is too large in diameter for heat treating, is made to converge by the two mirrors, oriented so as to compensate for astigmatism. Spot size and scan width are adjustable over a wide range, as is scan frequency, which is equal to mirror rotational frequency. The scan produces a uniform, time-averaged distribution of power on the work piece.

Journal ArticleDOI
TL;DR: In this article, the effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed, and the results are compared with experiment and the onset time for instability and the spindown time are given.
Abstract: A cylinder filled with a viscous, incompressible fluid is in an initial state of rigid-body rotation about its axis of symmetry. If the container is brought to rest impulsively, the resulting unsteady spin-down flow may be subject to sidewall instabilities due to an imbalance between centrifugal and pressure gradient forces. These instabilities are examined numerically using a finite-difference simulation to integrate the axisymmetric Navier–Stokes equations for a variety of aspect ratios and Reynolds numbers. The Taylor–Gortler vortex-wavelength spectrum, the torque and the angular momentum histories are calculated. Criteria for the onset time for instability and the spin-down time are given. The effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed. The results are compared with experiment.

Journal ArticleDOI
TL;DR: In this article, the vibration-rotation Raman spectrum of the ν2 fundamental band of P4 has been recorded photographically using a spectrograph with a reciprocal linear dispersion of 1.36 cm−1 mm−1.
Abstract: The vibration-rotation Raman spectrum of the ν2 fundamental band of P4 has been recorded photographically using a spectrograph with a reciprocal linear dispersion of 1.36 cm−1 mm−1. Analysis of the spectrum gave the following values for the vibration and rotation constants and the PP bond length:

Patent
21 Apr 1981
TL;DR: In this paper, a rotating mark carrier is placed on one of the two members to measure the angle between two members with respect to an axis of rotation about which they are rotatable with respect each other.
Abstract: The angle which two members enclose with respect to an axis of rotation about which they are rotatable with respect to each other is measured by placing a rotating mark carrier on one of two members. The carrier has marks disposed thereon at a certain distance apart in the direction of rotation. A first sensor is attached to the same member as the mark carrier and a second sensor is attached to the other member. The sensors emit a signal corresponding to each of the passing marks, which signal is fed to a measuring and evaluating circuit. The circuit has an identification circuit which identifies the marks belonging to the signals emitted by the sensors, a time measuring unit which measures the time distances of the signals emitted by the sensors and a calculation and storage circuit which, after receiving a corresponding command signal, calculates and stores the angular distances, with respect to a zero point of the angular measurements. The measurement is taken between the marks from the time distance values for signals assigned to identified marks and coming from the various sensors; from stored calibrating values for the absolute angular distances of identified marks; and from the instantaneous angular velocity of the mark carrier; said calculation and storage circuit, upon subsequent rotations of the mark carrier, calculates the instantaneous angle between the two members from the time distance values for signals assigned to identified marks and coming from the various sensors, and from the stored angular distances of these marks, the angular distances being with respect to the zero point of the angular measurement, and from the instantaneous angular velocity of the mark carrier.

Patent
15 May 1981
TL;DR: In this article, a robotic manipulator structure including a base supporting first and second independently operable drive motors 16 and 18, a first swinging arm rotatably supported by the base and driven from the first drive, and a second swinging arm 42 supported for rotation through a plane translationally displaced from the plane through which the first arm rotates, was presented.
Abstract: A robotic manipulator structure including a base supporting first and second independently operable drive motors 16 and 18, a first swinging arm rotatably supported by the base and driven from the first drive, a second swinging arm 42 supported for rotation at the end of the first arm for rotation through a plane translationally displaced from the plane through which the first arm rotates, and a mechanism for coupling the rotation of the second drive motor 18 through the hollow shaft 50 concentrically located and rotatable within the hollow shaft 38, and through a sprocket and chain arrangement in the hollow 58 of the first arm to independently effect the rotation of the second arm 42

Journal ArticleDOI
TL;DR: In this paper, a model for simulating the condensed phase of SF6 is developed, using a potential function which is satisfactory in lattice statics and which gives, as required, an unstable performance in the lattice dynamics.
Abstract: A model for simulating the condensed phase of SF6 is developed, using a potential function which is satisfactory in lattice statics and which gives, as required, an unstable performance in lattice dynamics. A sample of 54 molecules is used, in which the molecular motion is restricted to angular displacements only. Molecular orientation is described by the quaternion formulation, into which the molecular symmetry operations are worked. The quaternion parameters are altered whenever a molecule reorients on its site, and a record is kept of every such event. The extra energy associated with molecular reorientation is normally passed on to a nearest neighbour which may then undergo a rotation, more often about a perpendicular axis. This cooperative motion is described using a topological diagram. Future calculations on the DAP are suggested.

Patent
16 Dec 1981
TL;DR: In this article, a rotation index mark is provided to indicate a rotation starting point where the rotation index marks are constructed of a grooved-like phase structure, which can be formed in a track which is located separated from the information recording tracks, and may be detected optically without using a laser light beam.
Abstract: In an optical recording disk having groove-like guide tracks, a rotation index mark is provided to indicate a rotation starting point where the rotation index mark is constructed of a grooved-like phase structure. The rotation index mark may be formed in a track which is located separated from the information recording tracks, and may be detected optically without using a laser light beam. The rotation index mark is used to control the rotation of the disk as well as writing and reading operation of an optical disk recording/reproducing apparatus so that various information, such as video signals, can be accurately recorded and reproduced. In the case of recording digital signals, the guide tracks may be divided into a plurality of sector regions, and sector index marks corresponding to respective sector regions may also be formed together with the rotation index mark. Furthermore, an address index mark indicative of the position of track address region radially formed in the guide tracks may also be added.