Principle Of Angular Momentum Research Articles

Rigid-Flexible Coupled Dynamic and Control for Thermally Induced Vibration and Attitude Motion of a Spacecraft with Hoop-Truss Antenna

As space exploration activities are developing rapidly, spacecraft with large antennas have gained wide acceptance in providing reliable telecommunications and astrophysical observations. In this paper, the dynamic responses and control strategy for a spacecraft with a large hoop-truss antenna under solar flux shock are studied. According to the momentum and angular momentum principle, the rigid-flexible coupled rotational dynamic equation and the translational dynamic equation of the system are established, which include the attitude motion of the rigid main body and the vibration of the antenna. Then, a finite element model of the antenna is established to analytically obtain the corresponding vibration modal shape matrix and natural frequencies. Last, the coupled responses for the attitude motion and vibration are investigated. The corresponding control strategy is designed based on a double-loop structure sliding mode control method. The Lyapunov method is used to demonstrate the global asymptotic stability of the system. Simulations verify the effectiveness of the proposed rigid-flexible coupled model and control strategy.

Detumbling a Non-Cooperative Tumbling Target Using a Low-Thrust Device

This paper presents a new detumbling strategy for non-cooperative tumbling targets using a low-thrust device. The device with a harpoon on the front is released from the servicing satellite and embedded in the target. Then, the device’s thrusters are used to reduce the target’s angular velocity. In this paper, an impact model between the target and the device is established based on the conservative principle of linear and angular momentum. The dynamic equation of the combined system after impact is derived based on the principle of virtual power. A detumbling control scheme combining the linear quadratic regulator (LQR), pulse-width pulse-frequency (PWPF) modulation, and particle swarm optimization (PSO) is developed. The continuous optimal control signal obtained by LQR is transformed into a series of pulse signals by a PWPF modulator. To improve the performance of the detumbling controller, the weighting matrices of LQR are optimized by PSO, and two constrained optimization problems are studied. Finally, the effectiveness and robustness of the proposed strategy are verified by numerical simulations.

CFD tool application in predicting the behavior of a centrifugal fan designed by one-dimensional theory

Computational fluid dynamics (CFD) is the most current technology in the fluid flow study. Experimental methods for predicting the turbomachinery performance involve greater time consumption and financial resources compared to the CFD approach. The purpose of this article is to present the analysis of CFD simulation results in a centrifugal fan. The impeller was calculated using the one-dimensional theory and the volute the principle of constant angular momentum. The ANSYS-CFX software was used for the simulation. The turbulence model adopted was the SST. The simulation provided the characteristic curves, the pressure and velocity distribution, and the static and total pressure values at impeller and volute exit. An analysis of the behavior of the pressure plots, and the loss and recovery of pressure in the volute was performed. The results indicated the characteristic curves, the pressure and velocity distribution were consistent with the turbomachinery theory. The pressure values showed the static pressure at volute exit was smaller than impeller exit for some flow rate. It caused the pressure recovery coefficient negative. This work indicated to be possible design a centrifugal fan applying the one-dimensional theory and optimize it with the CFD tool.

A comprehensive analysis of factors affecting the accuracy of the precision hydrostatic spindle with mid-thrust bearing layout

This paper investigates the influence of rotor coaxiality error on spindle accuracy under different operating conditions in the precision hydrostatic spindle with a mid-thrust bearing structure. Firstly, a linearized model of rotor dynamics equation with five degrees-of-freedom is established based on Newton’s law of motion and angular momentum principle. Then, by solving the Reynolds equation and the flow continuity equation using the mathematical perturbation method, the steady and transient pressure distribution functions of the hydrostatic bearings are obtained; subsequently, the stiffness and damping coefficient matrices of the spindle are determined. Furthermore, the linearized stiffness and damping coefficients are substituted into the rotor dynamics equation to obtain the instantaneous acceleration of the rotor, and the motion trajectory of the rotor is solved iteratively by the Euler method. Finally, the paper studies the influences of different rotor coaxiality, rotating speed, cutting load, oil supply pressure, and oil film clearance on dynamic characteristics, amplitude amplification factor, and radial runout of the spindle by computer simulation. The simulation results show that the spindle runout is more sensitive to rotor coaxiality error and oil film clearance.

A Survey of Orbital Angular Momentum in Wireless Communication

Electromagnetic vortices are introduced into wireless communication to improve spectral efficiency and anti-interference capability. In this paper, the basic principle and characteristics of Orbital Angular Momentum (OAM) and electromagnetic eddy are introduced firstly. The principle of generating Orbital Angular Momentum from supersurface is given, and the methods and research status of generating orbital angular momentum based on supersurface are summarized. The transmission performance, receiving and detecting method, multiplexing and demultiplexing performance of orbital angular momentum are summarized. Finally, the key problems to be solved in the future application of wireless communication orbital angular momentum are discussed.

Fast modelling and simulation of the dynamic behaviour of a wet multidisc clutch during the engagement phase

In recent years multidisc wet friction clutches are of great importance to manufacturers of automatic transmissions (ATs) for the automotive industry, particularly since the introduction of double-clutched ATs. Their main advantage compared to their dry-friction counterparts is that they ensure smooth engagement, high reliability and long service life. Their progressive engagement due to the developed Couette flow between the discs enables them to be used both as clutches and as brakes in order to control power flow in simultaneously engaged geared shafts in the AT. Due to the coupled nature between the mechanical and the fluid dynamics regimes governing their operation, these systems are highly complex to be treated analytically and instead numerical approaches have proven to provide better results. However, the numerical treatment of such problems provides only case-specific results, which cannot be generalised and are not able to provide a general insight in the complex dynamics of the device. Furthermore the computational cost and the associated modelling and simulation effort during the design phase is high, making the incorporation of such methods in iterative design processes and algorithms counterproductive. In this paper the modelling of the dynamic behaviour of a wet multidisc clutch during the engagement phase is performed, via the combination of analytical and numerical methods and conclusions are drawn about the effect of the main geometric, kinematic and dynamic design parameters on the clutch’s response. The dynamic modelling is performed by applying the principle of linear and angular momentum on each disc. The effect of the fluid film is taken into account through the solution of the governing Navier-Stokes equations via CFD analysis or by the use of semi-analytical solutions with high accuracy, where applicable. Therefore both the developed pressure field and the torque of the fluid film are calculated efficiently and used in the simulation of the system. The flow is assumed to be laminar and the discs rigid and flat.

Relative Attitude Dynamics and Control of Spacecraft Formation Flying Considering Flexible Panels

As a key technology for orbital applications, researches on spacecraft formation flying (SFF) attract more attention. However, most of existing researches about dynamics and control of SFF focus on rigid spacecrafts without considering the effect of flexible attachments (such as flexible panels). In this paper, relative attitude dynamics and active control of SFF for a flexible spacecraft (follower spacecraft) and a rigid spacecraft (target spacecraft) are investigated. Firstly, a dynamic model of the flexible spacecraft is established by the principle of angular momentum. Then, the equation of relative attitude dynamics between the flexible spacecraft and the rigid spacecraft is derived by the quaternion to represent the attitude relation of the two spacecrafts. Finally, an attitude feedback controller is designed for the SFF system, and its stability is proved by the Lyapunov stability theory. Simulation results indicate that the panel flexibility has an obvious influence on the dynamic behaviour of the system, the designed controller can effectively control the attitude of the two spacecrafts to achieve synchronization, and the elastic vibration of the panels may be suppressed simultaneously.

Utilizing the Momentum in Orbital Angular Momentum: Augmented OAM induced by a frac{{boldsymbol{pi }}}{{bf{2}}} Aperture of Three Elements

The feasibility to induce augmented dominant OAM modes by a π/2 aperture of three elements in space and weighted quasi-phase shifts is realised in this paper. It is shown through theory, numerical simulations and experimentation, that electromagnetic (EM) waves carrying non-integer OAM with dominant mode l = +1 in the microwave domain can be generated by a quarter of a full azimuthal annular aperture consisting of three elements and a weighted phase shift augmenting the expected conventional phase shift to reach Berry’s mode dominance theory of half integer l. With reference to the uncertainty principle of angular momentum and angular position, the proposed augmented OAM with weighted phase shift method seems to decrease mode uncertainties and augment mode dominance.

Spin memory effect for compact binaries in the post-Newtonian approximation

The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not been computed explicitly for astrophysical sources of gravitational waves, such as compact binaries. In this paper, we compute the spin memory in terms of a set of radiative multipole moments of the gravitational-wave strain. The result of this calculation allows us to establish the following results about the spin memory: (i) We find that the accumulation of the spin memory behaves in a qualitatively different way from that of the displacement memory effect for nonspinning, quasicircular compact binaries in the post-Newtonian approximation: the spin memory undergoes a large secular growth over the duration of the inspiral, whereas for the displacement effect this increase is small. (ii) The rate at which the spin memory grows is equivalent to a nonlinear, but nonoscillatory and nonhereditary effect in the gravitational waveform that had been previously calculated for nonspinning, quasicircular compact binaries. (iii) This rate of build-up of the spin memory could potentially be detected by future gravitational-wave detectors by carefully combining the measured waveforms from hundreds of gravitational-wave detections of compact binaries.

Dynamic analysis of water-lubricated motorized spindle considering tilting effect of thrust bearing

The dynamic modeling for the rotor with large diameter thrust bearings is one of the key issues in the design and operation of water-lubricated motorized spindle. In the machining process, the spindle not only translates along the x, y, z directions, but also tilts about the x and y axes under the cutting forces. As a result, the tilting effect of the thrust bearing on the dynamic performances of the motorized spindle should be considered. A five degree-of-freedom dynamic model for the spindle is established based on the Newton’s Laws and the principle of Angular Momentum. The translational and tilting dynamic coefficients for both the journal and thrust water-lubricated bearings were obtained by using Reynolds equation. The computed results show that the tilting effect of the thrust bearing on the dynamic performance of the motorized spindle should be considered when a large diameter thrust bearing is employed.

Effect of Inlet Clearance on the Aerodynamic Performance of a Centrifugal Blower

AbstractThe present work reports the effect of inlet clearance on the performance of a centrifugal blower, with parallel wall volute, over its full operating range. For a particular impeller configuration, four volutes based on constant angular momentum principle, have been designed and analysed numerically for varying inlet clearances ranging from 0 mm (ideal clearance) to 5 mm. The computational methodology is validated using experimental data. The results indicate that as the clearance increases, the impeller performance in terms of both static and total pressure rise deteriorate. Further, the stage performances deteriorate in terms of efficiency and specific work for all mass flow rates. However, the performance of volute improves at lower mass flow rates compared to the Best Efficiency Point (BEP). A set of correlations have been developed to predict the change in stage performance as a function of clearance ratio. The non-dimensional values of change in specific work, isentropic efficiency and static pressure are found to be same irrespective of the shape of the volute.

Principle of generalized velocities in dynamics of planar separation of a rigid body

In this paper, the dynamics of planar separation of a rigid body into two rigid bodies is investigated. Motion of the initial body is planar and its properties (position, velocity, angular velocity, and angular position) are exactly known before separation. The process of separation lasts for a short time during which it is assumed that the position and angle position of the bodies do not vary. After separation, the separated and the remainder body remain to move planar. Applying the principle of momentum and angular momentum, velocity and angular velocity of the separated and remainder body are calculated. In the paper, the analytical procedure for determining these values is developed. Introducing the virtual velocity and angular velocity, the modified D’Alembert–Lagrange equation for planar separation of a body is expressed. Virtual works of impulses caused by impact force and torque are defined and discussed. Using the generalized velocity and angular velocity and introducing the generalized impulse, modified Lagrange’s equations for planar separations are obtained. In this paper, an example of separation of a planar beam on which an impulse of impact force acts is analyzed. Applying the suggested equations, velocity and angular velocity of the remainder beam are determined and discussed. Conditions for transformation of the planar motion into pure translatory motion of the remainder beam are determined. The obtained values represent the initial conditions for long term motion of the remainder part of the beam. The analytical methods suggested in the paper have the potential to improve our knowledge in dynamics of the discontinual separation of a rigid body. The obtained results have practical significance, too.

Erratum: “Applying the principle of angular momentum to constrained systems of point masses” [Am. J. Phys. 82, 165–168 (2014)

Erratum: “Applying the principle of angular momentum to constrained systems of point masses” [Am. J. Phys. <b>82</b>, 165–168 (2014)

Dynamic modeling and simulation for the rigid flexible coupling system with a non-tip payload in non-inertial coordinate system

The rigid flexible coupling system with a payload at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate system and the subsystem modeling principle, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are established via material mechanics and the angular momentum principle. This paper elucidates that dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. First, the payload at non-tip position is incorporated into the continuous dynamic equations of the system by means of the Dirac function and the Heaviside function. Then, the constrained modes of the flexible beam are analyzed. According to the boundary conditions of the constrained modes, a reasonable position interval of the payload is proposed. It corrects the inaccurate understandings in some papers. Finally, based on the conclusions of orthogonalization about the normal constrained modes, the finite dimensional state space model suitable for controller design is obtained. In addition, in order to make the finite dimensional dynamic model established more practical, based on the common constrained modes, the dimensionless variables and parameters are introduced, and the dimensionless finite dimensional dynamic model of the system is derived. The numerical simulation results show that: dynamic stiffening is included in the first-order dynamic model established in this paper, therefore, it can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately; the payload has a softening effect on the dynamic behaviors of the flexible beam, and the effect would be more obvious when the payload has a larger rotary inertia or a larger mass, or lies closer to the tip of the beam.

Applying the principle of angular momentum to constrained systems of point masses

An argument is presented to justify the application of the principle of angular momentum to systems of point masses that are constrained by massless internal connections.

Pigeons produce aerodynamic torques through changes in wing trajectory during low speed aerial turns.

The complexity of low speed maneuvering flight is apparent from the combination of two critical aspects of this behavior: high power and precise control. To understand how such control is achieved, we examined the underlying kinematics and resulting aerodynamic mechanisms of low speed turning flight in the pigeon (Columba livia). Three birds were trained to perform 90 deg level turns in a stereotypical fashion and detailed three-dimensional (3D) kinematics were recorded at high speeds. Applying the angular momentum principle, we used mechanical modeling based on time-varying 3D inertia properties of individual sections of the pigeon's body to separate angular accelerations of the torso based on aerodynamics from those based on inertial effects. Directly measured angular accelerations of the torso were predicted by aerodynamic torques, justifying inferences of aerodynamic torque generation based on inside wing versus outside wing kinematics. Surprisingly, contralateral asymmetries in wing speed did not appear to underlie the 90 deg aerial turns, nor did contralateral differences in wing area, angle of attack, wingbeat amplitude or timing. Instead, torso angular accelerations into the turn were associated with the outside wing sweeping more anteriorly compared with a more laterally directed inside wing. In addition to moving through a relatively more retracted path, the inside wing was also more strongly pronated about its long axis compared with the outside wing, offsetting any difference in aerodynamic angle of attack that might arise from the observed asymmetry in wing trajectories. Therefore, to generate roll and pitch torques into the turn, pigeons simply reorient their wing trajectories toward the desired flight direction. As a result, by acting above the center of mass, the net aerodynamic force produced by the wings is directed inward, generating the necessary torques for turning.

Reply to “Comment on ‘Hydrodynamics of fractal continuum flow’ and ‘Map of fluid flow in fractal porous medium into fractal continuum flow’ ”

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

Attitude maneuver of liquid-filled spacecraft with a flexible appendage by momentum wheel

Attitude maneuver of liquid-filled spacecraft with an appendage as a cantilever beam by momentum wheel is studied. The dynamic equations are derived by conservation of angular momentum and force equilibrium principle. A feedback control strategy of the momentum wheel is applied for the attitude maneuver. The residual nutation of the spacecraft in maneuver process changes with some chosen parameters, such as steady state time, locations of the liquid container and the appendage, and appendage parameters. The results indicate that locations in the second and fourth quadrants of the body-fixed coordinate system and the second quadrant of the wall of the main body are better choices for placing the liquid containers and the appendage than other locations if they can be placed randomly. Higher density and thicker cross section are better for lowering the residual nutation if they can be changed. Light appendage can be modeled as a rigid body, which results in a larger residual nutation than a flexible model though. The residual nutation decreases with increasing absolute value of the initial sloshing angular height.

Students’ Perceptions of Dynamics Concept Pairs and Correlation with Their Problem-Solving Performance

A concept pair is a pair of concepts that are fundamentally different but closely related. To develop a solid conceptual understanding in dynamics (a foundational engineering science course) and physics, students must understand the fundamental difference and relationship between two concepts that are included in each concept pair. However, all existing research in dynamics and physics education has been focused on the identification and repair of students’ misunderstanding of individual concepts, but not concept pairs. The present research fills the gap of existing research by studying students’ perceptions of dynamics concept pairs and correlation with their problem-solving performance in both particle and rigid-body dynamics. A total of 88 engineering undergraduate students participated in the present study. Students’ perceptions were assessed using a 40-item instrument that included 20 dynamics concept pairs at fundamental Level One and higher-order Level Two. Students’ problem-solving performance was assessed using four exams that included 66 dynamics problems. The coefficients of reliability (Cronbach’s α) of assessment instruments vary between 0.69 and 0.93. The research findings from the present study show that students were not confident in their understanding of Level-Two concept pairs, especially the relationship between the Principle of Linear Impulse and Momentum and the Principle of Angular Impulse and Momentum, and the relationship between the Principle of Angular Impulse and Momentum and the Conservation of Angular Momentum. A statistically significant correlation exists between students’ perceptions of Level-Two concept pairs and their problem-solving performance on both particle dynamics (r = 0.355, p < 0.01) and rigid-body dynamics (r = 0.351, p < 0.01). The research findings made from the present study imply that educational efforts should be focused on improving students’ understanding of Level-Two dynamics concept pairs.

Shaking Moment Optimum Balancing of Planar Mechanisms

A new method of shaking moment balancing of force balanced linkages is presented in this paper. The shaking moment balancing is gained based on the angular momentum principle. The method of synthesizing a dyad to balance the shaking moments is given, two kinds of structure types are calculated, all the maximum absolute values of the shaking moments are decreased by more than 75 % and the f1uctuation values of those are reduced by more than 68 %.