Nutation Angle Research Articles

A precessing and nutating beam with a tip mass

Stability analysis of elastic vibration of a simultaneously precessing and nutating beam with a tip mass is attempted here. A simple two-degree of freedom model is considered to have an understanding of the terms appearing in the parametric equations with precession softening and centrifugal stiffening. The stability margin is determined using a variant of Hill's method using precession and nutation speeds as parameters. It is found that the stability of an only precessing beam depends on the inclination of the beam-centerline with the axis of precession. A precessing beam with very slow nutation is unstable because of its passage through a particular range of nutation angle.

Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral

AbstractThe free-fall motion of a thin disk with small dimensionless moments of inertia (${I}^{\ast } \lt 1{0}^{- 3} $) was investigated experimentally. The transition from two-dimensional zigzag motion to three-dimensional spiral motion occurs due to the growth of three-dimensional disturbances. Oscillations in the direction normal to the zigzag plane increase with the development of this instability. At the same time, the oscillation of the nutation angle decreases to zero and the angle remains constant. The effects of initial conditions (release angle) were investigated. Two kinds of transition modes, zigzag–spiral transition and zigzag–spiral–zigzag intermittence transition, were observed to be separated by a critical Reynolds number. In addition, the solution of the generalized Kirchhoff equations shows that the small ${I}^{\ast } $ is responsible for the growth of disturbances in the third dimension (perpendicular to the planar motion).

Influence of shell initial perturbational motion conditions on its nutation angle value

The article investigates the influence of initial conditions of projection of a shell from a cannon bore providing that cannon bore and shell have perfect axial symmetry, and shell precessional motion occurs only due to gravity action, as well as gun tube substantial wear and warming up when firing. Dependancies, allowing to evaluate influence of initial conditions of projection of a shell from a cannon bore because of the diverse state of shell and bore have been given.

Attitude manoeuvre of spacecraft with long cantilever beam appendage by momentum wheel

Attitude manoeuvre of spacecraft with a long cantilever beam appendage by momentum wheel is studied. The dynamics equation of the main body is derived by conservation of angular momentum. The dynamics equation of the appendage is derived by force equilibrium principle. Two feedback control strategies of the momentum wheel are applied for the attitude manoeuvre of the main body. The lateral vibration of the appendage is suppressed by active control in proportion to its lateral displacement and velocity. The variation of residual nutation angle of the spacecraft or the residual transversal angular velocity of the main body in the manoeuvre process is researched with changes of steady state time of the manoeuvre, appendage parameters, control parameters on the appendage and appendage location. In addition, spacecraft response is researched when there are no active controls on the appendage.

Study of Wheel Activated Gyroscopic-like Motion in Spacecraft Rotational Dynamics

This research investigates the applications of a gyroscopic-like motion embedded in the attitude dynamics of a rigid-body that can be induced with an onboard torque wheel. The motion may be utilized by a rigid spacecraft to regain its attitude stability from a tumbling or a flat-spin situation to rotate about a designated principal axis, which parallels to the spin axis of the torque wheel. Also, the total angular momentum of the spacecraft remains conserved during the process as disturbance torques around the system in space are considered relatively very small and are ignored. To start the motion, the wheel is manipulated to rotate the spacecraft platform with reaction torque such that the projection of the total angular momentum falls in a proper quadrant on the plane perpendicular to the designated principal axis. Then, the projection is able to activate a self-induced, gyroscopic- like motion, which in effect transfers angular momentum to the wheel and the platform along the designated principal axis, aligning the designated principal axis with the total angular momentum and reducing the nutation angle between the two to zero. The phenomenon can be derived from the attitude model in terms of angular momentum. The control law of the wheel torque is formulated with the method of feedback linearization following the results from the Lyapunov stability analysis. Without any direct control effort, simulation results indicate that efficient time and energy can be achieved with effective attitude recovery of a spacecraft to any of the principal axis compared to the existing methods, and the wheel momentum accumulated during the motion can be predicted after the alignment maneuver.

Micromotion Parameter Estimation of Free Rigid Targets Based on Radar Micro-Doppler

In this paper, an estimation method of micromotion parameters for free rigid targets using micro-Doppler (mD) features is investigated. These parameters include spin rate, precession rate, nutation angle, and inertia ratio. They represent the microdynamic characteristics and intrinsic properties of targets. The time variation of mD frequency is found complicated yet valuable to estimate the micromotion parameters. From the viewpoint of the spectra of mixed mD time-frequency (TF) data sequences, the theoretical analysis and mathematical derivation are conducted in detail according to the scatterer distribution of rigid bodies. We then present an approach to realize the micromotion parameter estimation from radar mD echoes. It mainly consists of TF transform, TF image processing, mixed mD TF data sequence formation, and spectral estimation. Simulation experiments and result discussion are carried out to demonstrate the effectiveness of the proposed estimation method.

Magnetic Attitude Control of Dynamically Unbalanced Spinning Spacecraft during Orbit Raising

AbstractIn this article, the use of a magnetic attitude control system (MACS) in preparing a spacecraft for orbit circularization without the use of high-level torque-restoring actuators is investigated. The main task of the attitude control subsystem is to maneuver the spacecraft so that its spin axis direction aligns with the direction of its velocity at the apogee place and to execute the spacecraft spin up for orbit circularization. The attitude control system is required to provide a desired attitude for maneuvering, such that the relevant maneuvers can be accomplished sequentially and successively at the apogee point. The nutation angle control system has been designed to maintain the nutation angle to less than 10° during orbital maneuvers. The magnitude of thrust force, duration of thrust application in each maneuver, and spin rate are chosen in such a way that the desired attitude of the satellite is not affected by maneuver-induced disturbances. This selection has been finalized through repeated...

Statistical analysis for rotational motion of a light descent capsule under deployment of a space cable system

The results of the statistical analysis for the rotational motion of a light descent capsule under deployment of the orbital cable system are presented. At mathematical simulation a cable is considered to be a weightless inextensible mechanical linkage. The cable is deployed according to the predetermined law. The basic spacecraft is oriented along the local geovertical by means of its own stabilization system. The simulation is carried out by the statistical testing method. The motion characteristics being studied include: modulus of the capsule angular velocity and the nutation angle at the final point of the cable deployment.

Multislice 1H MRSI of the human brain at 7 T using dynamic B0 and B1 shimming

Proton MR spectroscopic imaging of the human brain at ultra-high field (≥7 T) is challenging due to increased radio frequency power deposition, increased magnetic field B(0) inhomogeneity, and increased radio frequency magnetic field inhomogeneity. In addition, especially for multislice sequences, these effects directly inhibit the potential gains of higher magnetic field and can even cause a reduction in data quality. However, recent developments in dynamic B(0) magnetic field shimming and dynamic multitransmit radio frequency control allow for new acquisition strategies. Therefore, in this work, slice-by-slice B(0) and B(1) shimming was developed to optimize both B(0) magnetic field homogeneity and nutation angle over a large portion of the brain. Together with a low-power water and lipid suppression sequence and pulse-acquire spectroscopic imaging, a multislice MR spectroscopic imaging sequence is shown to be feasible at 7 T. This now allows for multislice metabolic imaging of the human brain with high sensitivity and high chemical shift resolution at ultra-high field.

Singularity Analysis of Limited-DOF Parallel Manipulator Based on Jacobian Matrixes

To analyze effects of singularity on parallel manipulator, the Jacobian matrixes were introduced as the indexes for analyzing the 3UPS/S parallel machine. The relationship between the velocity Jacobian matrix and the force-transformation matrix was established, and their equivalence was verified through the determinant and condition number’ reciprocal of the matrixes. Effects of singularity on motion accuracy, actuator forces and constrained forces were investigated within the nutation angle’range. The result showed that velocity analysis and mechanical analysis were consistent for 3UPS/S parallel machine in the aspect of singularity, and proved that the accuracy and actuator force properties were deteriorated when approach to singularity. The approach could be applied to other parallel manipulators in the research on singular problem as a reference.

Statics Analysis of the Mechanical Model of Nucleosome

Mechanical model of nucleoside and its equilibrium equations are set up, and the mechanical properties on the equilibrium position are analyzed. In the case constraint force and electrostatic attraction between cylinder OH and elastic rod are balanced, the analytic expression of nutation angle of the section and its conditions of existence are given. It is show that the cylinder OH can maintain equilibrium at any range of the precession angle. In the other case when unbanced, there is phenomenon of separation of elastic rod from cylinder OH in the spiral wound 2 circles, and numerical solution of the precession angle at separation points are calculated. Analysis of equilibrium of cylinder H1 illustrates that the generatrix of cylinder H1 and OH are not parallel, and the angle between them is obtained

Orientation of cylindrical particles in gas–solid circulating fluidized bed

The orientation of cylindrical particles in a gas–solid circulating fluidized bed was investigated by establishing a three-dimensional Euler–Lagrange model on the basis of rigid kinetics, impact kinetics and gas–solid two-phase flow theory. The resulting simulation indicated that the model could well illustrate the orientation of cylindrical particles in a riser during fluidization. The influences of bed structure and operation parameters on orientation of cylindrical particles were then studied and compared with related experimental results. The simulation results showed that the majority of cylindrical particles move with small nutation angles in the riser, the orientation of cylindrical particles is affected more obviously by their positions than by their slenderness and local gas velocities. The simulation results well agree with experiments, thus validating the proposed model and computation.

Photometric observations of 107P/Wilson–Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson–Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson–Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L 1: L 2: L 3 = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson–Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L 1: L 2: L 3 = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson–Harrington is C-type. No clear rotational color variations are confirmed on the surface.

Realignment capability of the nCPMG sequence

The nCPMG sequence is based on a particular phase modulation of the refocusing pulse train, and was originally designed for rendering the spin echo amplitude insensitive to the initial magnetization phase. This pulse sequence has the peculiarity of being easily invertible, which enables perfect driven equilibrium experiments, in the absence of relaxation. This magnetization ‘realignment’ is effective for all three components. Hence the overall operation is transparent. Supporting theory is presented here, together with the first direct experimental proof of the claim. The experiment shows that, with the present stabilization sequence, perfect realignment is indeed made possible for a range of refocusing pulse nutation angles from 130° to 230°.

Analysis of the accuracy of prediction of the celestial pole motion

VLBI observations carried out by global networks provide the most accurate values of the precession-nutation angles determining the position of the celestial pole; as a rule, these results become available two to four weeks after the observations. Therefore, numerous applications, such as satellite navigation systems, operational determination of Universal Time, and space navigation, use predictions of the coordinates of the celestial pole. In connection with this, the accuracy of predictions of the precession- nutation angles based on observational data obtained over the last three years is analyzed for the first time, using three empiric nutation models---namely, those developed at the US Naval Observatory, the Paris Observatory, and the Pulkovo Observatory. This analysis shows that the last model has the best of accuracy in predicting the coordinates of the celestial pole. The rms error for a one-month prediction proposed by this model is below 100 microarcsecond.

Flip-angle measurement by magnetization inversion: Calibration of magnetization nutation angle in hyperpolarized 3 He magnetic resonance imaging lung experiments

The aim of this work was to establish a new, fast, and robust method of flip-angle calibration for magnetic resonance imaging of hyperpolarized (3) He. The method called flip-angle measurement with magnetization inversion is based on acquiring images from periodically inverted longitudinal magnetization created using the spatial modulation of magnetization technique. By measuring the width of the area where the magnetization was inverted by the spatial modulation of magnetization preparation in phase images, the flip angle can be generated using a simple equation. To validate and establish the limits of the proposed method, flip-angle measurement with magnetization inversion acquisitions were simulated and applied to proton and hyperpolarized (3) He phantoms. Then, the calibration procedure was applied during hyperpolarized (3) He magnetic resonance imaging in a healthy volunteer. The advantage of the flip-angle measurement with magnetization inversion method compared with the conventional method based on the assessment of radiofrequency-decay is that it is free of errors induced by relaxation due to oxygen, by imperfect excitation slice profile and by any diffusion of (3) He into and out of the slice. Another advantage is that it does not require image processing with external software and therefore can be performed using the implemented tools on the magnetic resonance workstation.

Coning Motion of Spinning Missiles Induced by the Rate Loop

Rate loops are commonly employed to compensate damping for missiles due to their great effectiveness. However, unexpected coning instability could be induced when the missile is subjected to spinning. The stability condition of coning motion as well as suitable design criteria for spinning missiles with rate loop feedback is established in this paper. Based on the theory of nutation movement, nonlinear equations of motion in terms of the nutation and precession angles are created. The mathematic model of the actuator acting on spinning missiles is also derived. After introducing the complex angle of attack into the system, the governing equations can be simplified to an analytically solvable second-order differential equation with respect to this variable. The proposed method is demonstrated by numerical simulations. It is also found that the upper limit of the critical gain in the damping loops' feedback for the stability decreases dramatically with a spinning missile. The dynamic inverse technique is employed as a remedy and it shows great effectiveness and applicability for the problem discussed in this paper.

Research of impact of nutational fluctuations of shells (mines) on their flight range

The article contains the research of impact of nutational fluctuations of shells (mines) on their weight centre move trajectory. There are results of calculations of range errors caused by nutational fluctuations under various levels of impact of disturbing factors for 203-mm SPG 2S7, 152-mm SPG 2S5 and 240-mm SPM 2S4. There are results of calculations of distance of nutational fluctuations fading and the character of change of forming components and total angle of nutation for different types of shells (mines) depending on flight period is given.

Transmission Ratio Analysis and Controllable Tooth Profile Modeling for the Nutation Drive with Double Circular-Arc External and Internal Spiral Bevel Gears

This paper proposes an approach for calculating the transmission ratio of nutation drive based on the working principle of the nutation movements. Then, the analysis of the influences for the nutation angle on the transmission ratio is carried out. The controllable tooth profile modelling for external and internal spiral bevel gears with double circular-arc is proposed. Based on the proposed tooth profile modeling, the three dimensional modeling and virtual assembly of the nutation drive have been further completed. Finally, the kinematical simulation is preceded in the simulating system and the comparative results have been accomplished between the simulation results and the theoretical ones of the transmission ratio.

Analysis of attitude motion evolutions of variable mass gyrostats and coaxial rigid bodies system

Abstract This work involves the research into angular motion of variable mass gyrostats, coaxial bodies systems and dual-spin spacecraft in a translating coordinate frame. The variability of mass–inertia parameters of coaxial bodies causes non-trivial changes of system angular motion. The article describes qualitative method for phase space analysis, based on the evaluation of a phase trajectory curvature. The method can be used to investigate the phase trajectory shape and to synthesize conditions for special motion modes realization (for example, monotone decreasing/increasing of nutation angle). The paper results can be used to describe the motion of a variable mass dual-spin spacecraft, performing active maneuvers.