Showing papers on "Angular velocity published in 2000"

Presupernova Evolution of Rotating Massive Stars. I. Numerical Method and Evolution of the Internal Stellar Structure

Abstract: The evolution of rotating stars with zero-age main-sequence (ZAMS) masses in the range 8-25 M☉ is followed through all stages of stable evolution. The initial angular momentum is chosen such that the star's equatorial rotational velocity on the ZAMS ranges from zero to ~ 70% of breakup. The stars rotate rigidly on the ZAMS as a consequence of angular momentum redistribution during the pre-main-sequence evolution. Redistribution of angular momentum and chemical species are then followed as a consequence of Eddington-Sweet circulation, Solberg-Hoiland instability, the Goldreich-Schubert-Fricke instability, and secular and dynamic shear instability. The effects of the centrifugal force on the stellar structure are included. Convectively unstable zones are assumed to tend toward rigid rotation, and uncertain mixing efficiencies are gauged by observations. We find, as noted in previous work, that rotation increases the helium core masses and enriches the stellar envelopes with products of hydrogen burning. We determine, for the first time, the angular momentum distribution in typical presupernova stars along with their detailed chemical structure. Angular momentum loss due to (nonmagnetic) stellar winds and the redistribution of angular momentum during core hydrogen burning are of crucial importance for the specific angular momentum of the core. Neglecting magnetic fields, we find angular momentum transport from the core to the envelope to be unimportant after core helium burning. We obtain specific angular momenta for the iron core and overlying material of 1016-1017 cm2 s-1. These values are insensitive to the initial angular momentum and to uncertainties in the efficiencies of rotational mixing. They are small enough to avoid triaxial deformations of the iron core before it collapses, but could lead to neutron stars which rotate close to breakup. They are also in the range required for the collapsar model of gamma-ray bursts. The apparent discrepancy with the measured rotation rates of young pulsars is discussed.

Self-similar accretion flows with convection

Abstract: We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing-length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R-1/2, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions that lie in between the two limits. When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as ρ ∝ R-3/2. When convection moves angular momentum inward, the result depends on the viscosity coefficient α. If α > αcrit1 ~ 0.05, we once again find the standard ADAF solution. For α < αcrit2 ~ αcrit1, however, we find a nonaccreting solution in which ρ ∝ R-1/2. We refer to this as a "convective envelope" solution or a "convection-dominated accretion flow." Two-dimensional numerical simulations of ADAFs with values of α 0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give ρ ∝ R-1/2, in good agreement with the convective envelope solution. The R-1/2 density profile is not a consequence of mass outflow. The relevance of these axisymmetric low-α simulations to real accretion flows is uncertain.

Angular velocity sensor

Abstract: PROBLEM TO BE SOLVED: To provide an angular velocity sensor of a small size and a light weight. SOLUTION: In an angular velocity sensor, a fluid 9 is filled in a passage 41 for converting an angular acceleration to a flow speed of a fluid and a light wave guide oscillator 1 comprising an elastic body deformed and oscillated corresponding to the flow speed and having a light transmissivity is installed on the passage. A light of a light emitting device is wave-guided from a fulcrum side of the light wave guide oscillator and the light is radiated from a tip end of the light wave guide oscillator, i.e., a released end. A motion of the radiation point (or line) of the light is detected by a light-receiving device.

Rigid and differential plasma crystal rotation induced by magnetic fields

Abstract: Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution) When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces For the special case of rigid-body rotation, the confining potential is reconstructed Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid Further development is suggested in order to quantitatively implement these ideas

Rigid body attitude tracking without angular velocity feedback

Abstract: In this paper, we revisit the classical problem of attitude tracking for a rigid body. The interesting difference in the formulation is the assumption that only attitude measurements are available. We proceed to construct globally stabilizing control laws in terms of a minimal set of three-dimensional kinematic parameters that enable the rigid body to track any specified trajectory without requiring angular velocity measurements. The results presented here complement and extend some recent developments available for the nonminimal case of Euler parameters (quaternions).

Turbulent Molecular Cloud Cores: Rotational Properties

Abstract: The rotational properties of numerical models of centrally condensed, turbulent molecular cloud cores with velocity fields that are characterized by Gaussian random fields are investigated. It is shown that the observed line width-size relationship can be reproduced if the velocity power spectrum is a power law with P(k) ∝ kn and n = -3 to -4. The line-of-sight velocity maps of these cores show velocity gradients that can be interpreted as rotation. For n = -4, the deduced values of angular velocity Ω = 1.6 km s-1 pc-1×(R/0.1 pc)-0.5, and the scaling relations between Ω and the core radius R are in very good agreement with the observations. As a result of the dominance of long-wavelength modes, the cores also have a net specific angular momentum with an average value of J/M = 7 × 1020 × (R/0.1 pc)1.5 cm2 s-1 with a large spread. Their internal dimensionless rotational parameter is β ≈ 0.03, independent of the scale radius R. In general, the line-of-sight velocity gradient of an individual turbulent core does not provide a good estimate of its internal specific angular momentum. We find however that the distribution of the specific angular momenta of a large sample of cores which are described by the same power spectrum can be determined very accurately from the distribution of their line-of-sight velocity gradients Ω using the simple formula j = pΩR2, where p depends on the density distribution of the core and has to be determined from a Monte Carlo study. Our results show that for centrally condensed cores the intrinsic angular momentum is overestimated by a factor of 2-3 if p = 0.4 is used.

Three-dimensional data input device

Abstract: A three-dimensional data input device for a computer having a display screen includes a ball rotatably provided in a device body, and sensors for detecting rotation magnitudes of the ball along two axes on a plane and outputting displacement signals indicative of the detected rotation magnitudes, respectively. The device further includes a gyro for detecting an angular velocity of the device body about an axis extending at a given angle relative to the foregoing plane and outputting an angular velocity signal indicative of the detected angular velocity. The device further includes switches for outputting a selection signal in response to operation of at least one of selection buttons. The device derives displacement data based on the foregoing displacement signals and angular data based on the foregoing angular velocity signal and outputs the displacement data, the angular data and the selection signal to the computer. The computer moves a corresponding object on the screen on a plane corresponding to the displacement data and rotates the corresponding object corresponding to the angular data about one of given axes selected by the selection signal.

Turbulent Solar Convection and Its Coupling with Rotation: The Effect of Prandtl Number and Thermal Boundary Conditions on the Resulting Differential Rotation

Abstract: The dynamics of the vigorous convection in the outer envelope of the Sun must determine the transport of energy, angular momentum, and magnetic fields and must therefore be responsible for the observed surface activity and the angular velocity profile inferred helioseismically from SOI-MDI p-mode frequency splittings. Many different theoretical treatments have been applied to the problem, ranging from simple physical models such as mixing-length theory to sophisticated numerical simulations. Although mixing-length models provide a good first approximation to the structure of the convection zone, recent progress has mainly come from numerical simulations. Computational constraints have until now limited simulations in full spheres to essentially laminar convection. The angular velocity profiles have shown constancy on cylinders, in striking contrast to the approximately constant angular velocity on radial lines inferred for the Sun. In an effort to further our understanding of the dynamics of the solar convection zone, we have developed a new computer code that, by exploiting massively parallel architectures, enables us to study fully turbulent spherical shell convection. Here we present five fully evolved solutions. Motivated by the fact that a constant entropy upper boundary condition produces a latitudinal modulation of the emergent energy flux (of about 10%, i.e., far larger than is observed for the Sun), three of these solutions have a constant energy flux upper boundary condition. This leads to a latitudinal modulation of the specific entropy that breaks the constancy of the angular velocity on cylinders, making it more nearly constant on radial lines at midlatitudes. The effect of lowering the Prandtl number is also considered—highly time-dependent, vortical convective motions are revealed, and the Reynolds stresses are altered, leading to a reduced differential rotation. The differential rotation in all of our simulations shows a balance between driving by Reynolds stresses and damping by viscosity. This contrasts with the situation in the Sun, where the effect of viscosity on the mean differential rotation is almost negligible.

Rotation of horizontal-branch stars in globular clusters

Abstract: The rotation of horizontal-branch stars places important constraints on angular momentum evolution in evolved stars and therefore on rotational mixing on the giant branch. Prompted by new observations of rotation rates of horizontal-branch stars, we calculate simple models for the angular momentum evolution of a globular cluster giant star from the base of the giant branch to the star's appearance on the horizontal branch. We include mass loss and infer the accompanied loss of angular momentum for each of four assumptions about the internal angular momentum profile. Mass loss is found to have important implications for angular momentum evolution. These models are compared to observations of horizontal-branch rotation rates in M13. We find that rapid rotation on the horizontal branch can be reconciled with slow solid body main-sequence rotation if giant-branch stars have differential rotation in their convective envelopes and a rapidly rotating core, which is then followed by a redistribution of angular momentum on the horizontal branch. We discuss the physical reasons that these very different properties relative to the solar case may exist in giants. Rapid rotation in the core of the main-sequence precursors of the rapidly rotating horizontal-branch star or an angular momentum source on the giant branch is required for all cases if the rotational velocity of turnoff stars is less than 4 km s-1. We suggest that the observed range in rotation rates on the horizontal branch is caused by internal angular momentum redistribution, which occurs on a timescale comparable to the evolution of the stars on the horizontal branch. The apparent lack of rapid horizontal-branch rotators hotter than 12,000 K in M13 could be a consequence of gravitational settling, which inhibits internal angular momentum transport. Alternative explanations and observational tests are discussed.

Dynamics of a vortex in a trapped Bose-Einstein condensate

Abstract: We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

Winds from Accretion Disks Driven by Radiation and Magnetocentrifugal Force

Abstract: We study the two-dimensional, time-dependent hydrodynamics of radiation-driven winds from luminous accretion disks threaded by a strong, large-scale, ordered magnetic field. The radiation force is mediated primarily by spectral lines and is calculated using a generalized multidimensional formulation of the Sobolev approximation. The effects of the magnetic field are approximated by adding into the equation of motion a force that emulates a magnetocentrifugal force. Our approach allows us to calculate disk winds when the magnetic field controls the geometry of the flow, forces the flow to corotate with the disk, or both. In particular, we calculate models in which the lines of the poloidal component of the field are straight and inclined to the disk at a fixed angle. Our numerical calculations show that flows that conserve specific angular velocity have larger mass-loss rates than their counterparts that conserve specific angular momentum. The difference in the mass-loss rates between these two types of winds can be several orders of magnitude for low disk luminosities but vanishes for high disk luminosities. Winds that conserve angular velocity have much higher velocities than angular momentum-conserving winds. Fixing the wind geometry stabilizes winds that are unsteady when the geometry is derived self-consistently. The inclination angle between the poloidal velocity and the normal to the disk midplane is important. Nonzero inclination angles allow the magnetocentrifugal force to increase the mass-loss rate for low luminosities and increase the wind velocity for all luminosities. The presence of the azimuthal force does not change the mass-loss rate when the geometry of the flow is fixed. Our calculations also show that the radiation force can launch winds from magnetized disks. The line force can be essential in producing magnetohydrodynamical (MHD) winds from disks where the thermal energy is too low to launch winds or where the field lines make an angle of less than 30° with respect to the normal to the disk midplane. In the latter case the wind will be less decollimated by the centrifugal force near its base, and its collimation far away from the disk can be larger than the collimation of its centrifugally driven MHD counterpart.

A quaternion-based adaptive attitude tracking controller without velocity measurements

Abstract: The main problem addressed in this paper is the quaternion-based, attitude tracking control of rigid spacecraft without angular velocity measurements and in the presence of an unknown inertia matrix. As a stepping-stone, we first design an adaptive, full-state feedback controller that compensates for parametric uncertainty while ensuring asymptotic attitude tracking errors. The adaptive, full-state feedback controller is then re-designed such that the need for angular velocity measurements is eliminated. The proposed adaptive, output feedback controller ensures asymptotic attitude tracking.

Adaptive tracking control using synthesized velocity from attitude measurements

Abstract: The attitude tracking problem of uncertain rigid spacecraft without angular velocity measurements is addressed in the paper. The adaptive control law, which incorporates a velocity-generating filter from attitude measurements, is shown to ensure the asymptotic convergence of the attitude and angular velocity tracking errors despite unknown spacecraft inertia. Simulation results are presented to illustrate the theoretical results.

Dynamics of a vortex in a trapped Bose-Einstein condensate

Abstract: We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

Angular velocity sensor

Abstract: PROBLEM TO BE SOLVED: To provide an angular velocity sensor which is effective in a car-body control system, a navigation system or the like in a vehicle or the like which is comparatively low in cost and which can obtain a high sensitivity and a high detecting accuracy. SOLUTION: A single-crystal piezoelectric element material such as a crystal or the like is cut off to be an equilateral triangular pillar 11 so as to be fixed to an integral base or a separate base. An electrode A, an electrode B, an electrode C1 and an electrode C2 are formed on respective side faces of the equilateral triangular piller 11. An AC voltage is applied, from an oscillator OSC, across the electrode A and the electrode B. The equilateral triangular pillar 11 is driven in the direction of an arrow 17 so as to be set to be in an excitation state. The potential difference 15a and the potential difference 15b between the electrode C1 and the electrode C2 which are situated in a direction 18 which is at right angles to the excitation direction 17 are taken out from a differential amplifier 16, and the Coriolis force is detected. Since a driving vibrator and a detecting vibrator are constituted of an identical vibrator, respective resonance frequencies can be made to agree comparatively easily, an irregularity in a working operation or the like can be reduced thanks to the constitution of this angular velocity sensor, the sensor is comparatively low in cost, and the high sensitivity and the high detecting accuracy of the sensor can be obtained.

Non-axisymmetric vortices in two-dimensional flows

Abstract: Slightly non-axisymmetric vortices are analysed by asymptotic methods in the context of incompressible large-Reynolds-number two-dimensional flows. The structure of the non-axisymmetric correction generated by an external rotating multipolar strain field to a vortex with a Gaussian vorticity profile is first studied. It is shown that when the angular frequency w of the external field is in the range of the angular velocity of the vortex, the non-axisymmetric correction exhibits a critical-point singularity which requires the introduction of viscosity or nonlinearity to be smoothed. The nature of the critical layer, which depends on the parameter h = 1/(Re e3/2), where e is the amplitude of the non-axisymmetric correction and Re the Reynolds number based on the circulation of the vortex, is found to govern the entire structure of the correction. Numerous properties are analysed as w and h vary for a multipolar strain field of order n = 2, 3, 4 and 5. In the second part of the paper, the problem of the existence of a non-axisymmetric correction which can survive without external field due to the presence of a nonlinear critical layer is addressed. For a family of vorticity profiles ranging from Gaussian to top-hat, such a correction is shown to exist for particular values of the angular frequency. The resulting non-axisymmetric vortices are analysed in detail and compared to recent computations by Rossi, Lingevitch & Bernoff (1997) and Dritschel (1998) of non-axisymmetric vortices. The results are also discussed in the context of electron columns where similar non-axisymmetric structures were observed (Driscoll & Fine 1990).

Rotating Block Method for Seismic Displacement of Gravity Walls

Abstract: A rotating block method is developed to calculate the rotational displacements of gravity retaining walls based on rigid foundations under seismic loading. The method is similar to the pseudostatic sliding block method of Newmark. When a threshold acceleration for rotation is exceeded, a rigid wall will start to rotate until the angular velocity for rotation is reduced to zero. The influence of ground motion characteristics on computed wall deformation was evaluated. The procedure was validated by data from centrifuge tests. This method is also applicable for the most complex cases when the sliding and rotation of a gravity wall are coupled.

A Quaternion-Based Adaptive Attitude Tracking Controller Without Velocity Measurements'

Abstract: The main problem addressed in this paper is the quaternion-based, attitude tracking control of rigid spacecraft without angular velocity measurements and in the presence of an unknown inertia matrix. As a stepping-stone, we first de- sign an adaptive, full-state feedback controller that compensates for parametric uncertainty while ensuring asymptotic attitude tracking errors. The adaptive, full-state feedback controller is then redesigned such that the need for angular velocity measure- ments is eliminated. The proposed adaptive, output feedback controller ensures asymptotic attitude tracking.

Image stabilizing apparatus

Abstract: In an image stabilizing apparatus in which an actuator for pivoting gimbal suspension means is controlled by a feedback loop, the gain of feedback loop based on the angular position is enhanced when the angular velocity is at a first set value or higher until the angular velocity becomes a second set value or lower, whereby a panning mode is automatically attained when a pan/tilt operation is carried out. Also, the gain of feedback loop based on the angular position is enhanced when the angular velocity is enhanced until a lapse of a predetermined time after starting the pivoting control of the gimbal suspension means, whereby the behavior of gimbal suspension means is stabilized.

Stick-Slip and Bit-Bounce of Deep-Hole Drillstrings

Abstract: A mathematical model for the drilling process is derived and solved numerically as an initial value problem. The equations of motion are nonlinear differential equations for longitudinal, lateral, and rotational motion of the pipe as well as for the rate of flow and pressure of the mud. The model comprises a mud (Moineau) motor which rotates the bit relative to the lower end of the pipe. The model accounts for buckling of the pipe due to excessive torque and longitudinal forces, as well as for the effect of hydraulic pressure on the deformed pipe. Weight on bit and torque on bit are computed from characteristic curves which are functions of the penetration of the bit into the rock and the angular velocity of the bit. Numerical simulations show self-excited oscillations of the drillstring, including bit take-off from the bottom hole and large amplitudes in the bit's angular velocity.

Method for minimizing errors in sensors used for a recording apparatus of car accidents

Abstract: In a method for minimizing errors in sensors used for a recording apparatus of car accidents, data including acceleration, yaw-rate, vehicle speed measured at the transmission, and steering angle are first measured by sensors, then error in forward acceleration is corrected on the basis of vehicle speed measured at the transmission. Next, error in lateral acceleration is corrected on the basis of vehicle speed and steering angle measured by a steering angle sensor, then error in rotational angular velocity is corrected on the basis of steering angle and vehicle speed. Finally, data is recorded as corrected values.

Vehicle driving condition detection device

Abstract: A vehicle driving condition detection device is adapted to detect a vehicle running along a banked or laterally sloping road, as well as a lateral acceleration, and sideslip angle with good accuracy. The sideslip angle is estimated at a vehicle-body sideslip angle estimating circuit based on a steering angle δf, a lateral acceleration y, a yaw rate {dot over (θ)}, and a vehicle speed V. In addition, using a differentiating device, the estimated sideslip angle is differentiated to calculate a slip angular velocity. A subtracting device is provided at which a deviation is calculated between the slip angular velocity and a slip angular velocity detected at a slip angular velocity calculating circuit. The deviation can detect a banked or laterally sloping road due to the fact that the detected slip angular velocity at the slip angular velocity calculating circuit includes the gravity acceleration component that depends on the slope or bank of the road. Upon detecting a banked or sloping road, a deviation Δy (={dot over (θ)}·V−y) is outputted from a switching device, and at a subtracting device the detected lateral acceleration y is corrected by being subtracted with the deviation Δy. On the basis of the resultant or corrected lateral acceleration y, the vehicle-body sideslip angle is estimated. Such an estimation is made irrespective of the slope or bank of the road.

A vibrating piezoelectric ceramic shell as a rotation sensor

Abstract: Vibrations of a non-uniform circular cylindrical ceramic piezoelectric shell rotating about its axis are studied. It is shown that the shell can be used as a rotation sensor to measure the angular rate of a rotating body. Two-dimensional equations for a piezoelectric shell are employed. The sensitivity of the sensor and its dependence on various physical and geometric parameters are examined.

Artificial gravity as a countermeasure in long‐duration space flight

Abstract: Long-duration exposure to weightlessness results in bone demineralization, muscle atrophy, cardiovascular deconditioning, altered sensory-motor control, and central nervous system reorganizations. Exercise countermeasures and body loading methods so far employed have failed to prevent these changes. A human mission to Mars might last 2 or 3 years and without effective countermeasures could result in dangerous levels of bone and muscle loss. Artificial gravity generated by rotation of an entire space vehicle or of an inner chamber could be used to prevent structural changes. Some of the physical characteristics of rotating environments are outlined along with their implications for human performance. Artificial gravity is the centripetal force generated in a rotating vehicle and is proportional to the product of the square of angular velocity and the radius of rotation. Thus, for a particular g-level, there is a tradeoff between velocity of rotation and radius. Increased radius is vastly more expensive to achieve than velocity, so it is important to know the highest rotation rates to which humans can adapt. Early studies suggested that 3 rpm might be the upper limit because movement control and orientation were disrupted at higher velocities and motion sickness and chronic fatigue were persistent problems. Recent studies, however, are showing that, if the terminal velocity is achieved over a series of gradual steps and many body movements are made at each dwell velocity, then full adaptation of head, arm, and leg movements is possible. Rotation rates as high as 7.5-10 rpm are likely feasible. An important feature of the new studies is that they provide compelling evidence that equilibrium point theories of movement control are inadequate. The central principles of equilibrium point theories lead to the equifinality prediction, which is violated by movements made in rotating reference frames. Copyright 2000 Wiley-Liss, Inc.

5 – Flight dynamics and control

Abstract: Publisher Summary Degrees of freedom and fuselage of blade make flight dynamics and control look complicated. Before dealing with flight dynamics and dynamic stability problems analytically, it is important to consider the physical effects of velocity and angular rate disturbances on the helicopter. This chapter highlights all the disturbances affecting a helicopter: forward speed disturbance, vertical speed (incidence) disturbance, pitching angular velocity disturbance, sideslip disturbance, and Yawing disturbance. A helicopter is unstable both laterally and longitudinally in hovering flight, and the longitudinal instability becomes worse with increase of forward speed, particularly when the rotor has hinge-less blades. Tail plane is effective only in the upper half of the speed range. The unstable characteristics of the rotor deteriorate with speed and the tail plane becomes incapable of making the machine stable. Although adequate control power is available to correct disturbances, an unstable aircraft requires continuous correction and it is tiring to fly for long periods, even in calm weather. The stabilization devices fall into two categories: a mechanical/gyro device and automatic flight control systems.

Input device and control system

Abstract: PROBLEM TO BE SOLVED: To provide an input device improved in convenience and operability. SOLUTION: This input device is provided with a casing having a size capable of gripping in a human hand, a first angular velocity gyroscope 1x for supplying a first signal corresponding to the rotation of the casing at a first axial direction center and a second angular velocity gyroscope 1y for supplying a second signal corresponding to the rotation of the casing at a second axial direction center which is not parallel to the first axis. By outputting the first signal corresponding to the oscillation of the casing and outputting the second signal corresponding to the inclination of the casing, operation information can be inputted to prescribed equipment.

Rotation in liquid $^4$He: Lessons from a toy model

Abstract: This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid $^4$He. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of $\approx 10^3 - 10^4$ helium atoms. In particular, this model predicts, for the first time, the very large enhancement of the centrifugal distortion constants that have been observed experimentally. It also illustrates the different effects of increasing rotational velocity by increases in angular momentum quantum number or by increasing the rotational constant of the molecular rotor. It is found that fixed node, diffusion Monte Carlo and a hydrodynamic model provide upper and lower bounds on the size of the effective rotational constant of the molecular rotor when coupled to the helium.