Final Angular Velocity Research Articles

Synthesis of Nominal Reorientation Trajectories of a Small Satellite in Case of Failure of One Actuator

The paper devotes to the development of the approach for synthesis of reorientation trajectory of a small satellite. We consider the nanosatellite angular motion described by the kinematic quaternion equations. The aerodynamic and gravitational disturbance torques are taken into account in the angular motion model. Reorientation of a small satellite occurs from some initial position. In addition, the final angular velocity components do not exceed 0.1 °/s. The control program is given as the even Fourier series. The even Fourier series were chosen due to they can describe a complex dependency accurately. The coefficients of the even Fourier series are defined by the differential evolution algorithm. Previously, this approach has shown its efficiency for the cases of normal operation of the actuators. The paper presents the approach of synthesis of reorientation trajectory in case of failure of the actuator. The problem of reorientation reduces to optimization problem of searching of 34 coefficients of the even Fourier series that provided the achievement of the desired boundary conditions. The numerical results are given that approved the possibility of solution of the reorientation problem of small satellite in case of failure of the actuator. To compare the control programs, research was made between the cases of normal operation of the actuator and failure of the actuator. The value of the control torque differs by the order of magnitude in case of failure of the actuator. Despite this, its value is achievable for the magnetic coils.

Closed-form solution of attitude command generation for spin-to-spin maneuver

In recent earth observing missions, agile satellites enable various imaging modes beyond the traditional along-track strip imaging. However, it requires maneuvering with boundary conditions of considerable angular velocity, i.e., spin-to-spin maneuvering. This paper proposes an attitude command generation method for spin-to-spin maneuvering that can provide feedforward commands for the attitude control loop. A general solution for arbitrary flight time is provided which steers a satellite to the given final attitude and angular velocity at the prescribed time. In addition, an alternative method is proposed that further improves the maneuvering speed, which is applicable to small-angle maneuvering cases. The proposed solutions are both closed-form which are more intuitive and easier to comprehend than numerical solutions. It also has a great advantage in computational efficiency, which could enable its use on-board in real time. Numerical examples demonstrate the performance of the proposed methods in a single maneuvering case as well as in a consecutive maneuvering case integrated with a realistic earth observing scenario.

A close-form command shaping control for point-to-point maneuver with nonzero initial and final conditions

Command shaping algorithms are generally associated with nonzero initial and final conditions. However, initial disturbances may be inevitable, which compromises the effectiveness of shaped commands. A common example is when the crane’s jib is not or cannot be initially positioned directly above the payload, which forces the transfer operation to start with an initial angle. Shaped commands based on zero initial conditions would most probably result in unwanted oscillations at the target location of the transfer maneuver. Other applications may, by design, require nonzero final conditions such as the case of demolition cranes. In this work, a closed-form command shaping algorithm is developed considering nonzero initial angle and angular velocity disturbances. The algorithm is capable of setting the final angle and angular velocity to pre-determined design values. The equation of motion is derived and then solved to eliminate the associated residual vibrations using our proposed shaper. Using complex mathematical manipulations, the shapers parameters are derived analytically for the two cases; initial and final conditions. To test the proposed technique, several scenarios are simulated and tested experimentally. Simulation and experimental results illustrate the ability of the shaped command to either eliminate residual oscillations for nonzero initial conditions or conclude a maneuver at a pre-determined final angle value.

Effect of Footwear on the Biomechanics of Loaded Back Squats to Volitional Exhaustion in Skilled Lifters.

Brice, SM, Doma, K, and Spratford, W. Effect of footwear on the biomechanics of loaded back squats to volitional exhaustion in skilled lifters. J Strength Cond Res 36(10): 2676-2684, 2022-This study examined whether footwear influences the movement dynamics of barbell back squats to volitional exhaustion in experienced lifters. Eleven men (1 repetition maximum [1RM] = 138 ± 19 kg; 1RM % body mass = 168 ± 18%) performed 3 sets (5-12 ± 4 repetitions per set) of loaded barbell back squats to volitional exhaustion using raised-heel and flat-heel footwear. Barbell motion as well as moments, angles, angular velocity, and power in the sagittal plane at the ankle, knee, hip, and lumbopelvis were examined during the second repetition of the first set (T second ) and the final repetition of the third set (T final ). There were significant reductions ( p < 0.05) in lower-limb concentric angular velocity and power output for both footwear conditions. For the raised-heel condition at T final , hip and knee concentric angular velocities were significantly slower ( p < 0.05), and knee concentric power output was significantly less ( p < 0.05) compared with the flat-heel condition. A reduction in barbell velocity was not observed for the raised-heel condition despite there being reduction in hip and knee angular velocities. Furthermore, no differences were identified in lower-limb joint moments or any of the biomechanical characteristics of the lumbopelvis between the footwear conditions. The findings of this study suggest that neither type of footwear reduced joint loading or improved joint range-of-motion.

Benchmarking and validation of a combined CFD-optics solver for micro-scale problems

In this work, we present a new approach for coupled CFD-optics problems that consists of a combination of a finite element method (FEM) based flow solver with a ray tracing based tool for optic forces that are induced by a laser. We combined the open-source computational fluid dynamics (CFD) package FEATFLOW with the ray tracing software of the LAT-RUB to simulate optical trap configurations. We benchmark and analyze the solver first based on a configuration with a single spherical particle that is subjected to the laser forces of an optical trap. The setup is based on an experiment that is then compared to the results of our combined CFD-optics solver. As an extension of the standard procedure, we present a method with a time-stepping scheme that contains a macro step approach. The results show that this macro time-stepping scheme provides a significant acceleration while still maintaining good accuracy. A second configuration is analyzed that involves non-spherical geometries such as micro rotors. We proceed to compare simulation results of the final angular velocity of the micro rotor with experimental measurements.

Black hole geodesic parallel transport and the Marck reduction procedure

The Wigner rotations arising from the combination of boosts along two different directions are rederived from a relative boost point of view and applied to gyroscope spin precession along timelike geodesics in a Kerr spacetime, clarifying the geometrical properties of Marck's recipe for describing parallel transport along such world lines expressed in terms of the constants of the motion. His final angular velocity isolates the cumulative spin precession angular velocity independent of the spacetime tilting required to keep the spin 4-vector orthogonal to the gyro 4-velocity. As an explicit example the cumulative precession effects are computed for a test gyroscope moving along both bound and unbound equatorial plane geodesic orbits.

The ‘spinning disk touches stationary disk’ problem revisited: an experimental approach

A popular Newtonian mechanics problem, featured in textbooks, physics olympiads and forums alike, concerns two disks with different radii and moment of inertia that rotate differently and that touch each other. Most students struggle to calculate the final angular velocity of the disks, erroneously attempting to use different conservation laws. In this paper we propose a simple experiment that should help physics teachers explain this challenging exercise in an engaging way for the students. By using a smartphone/tablet and video analysis tools, the angular velocity of both disks can easily be tracked as a function of time, clearly showing the three stages of the interaction (before touching, only one disk rotating; touching with slippage; and touching without slippage). Processing and plotting of the data in a spreadsheet immediately shows which quantities are conserved and which are not. Several extensions to the core experiment are also suggested.

Translation and attitude synchronization for multiple rigid bodies using dual quaternions

In this paper, we investigate two attitude and translation synchronization problems for multiple fully actuated rigid bodies. A receiving little attention mathematical tool–dual quaternion is employed to design synchronization control laws. And the analysis based on dual quaternion is a unified solution for attitude and translation simultaneously. The definition and some properties about dual quaternion are introduced firstly. Then, a leaderless distributed control law is proposed for the attitude and translation synchronization of these rigid bodies with notion concision and non-singularity. Moreover, the final angular velocities and linear velocities are nonzero under the proposed control law if the synchronization is achieved. Next, we address the tracking synchronization for a group of rigid bodies with a time-varying leader. In addition, not only the synchronization performances under the acyclic communication topology are investigated, but the performances under the communication topology containing cycles are also analyzed. Finally, two examples are given to validate the effectiveness of the theoretical results.

Robust global bimodal rest-to-rest attitude control of rigid body using unit quaternion

This work proposes a hysteresis-based controller with two binary logic variables for the rest-to-rest control of attitude represented by quaternions. The control system has a hybrid nature given by the presence of a switching logic variable that indicates which quaternion representation of the reference attitude should be followed and by a second logic variable which indicates the chattering prone region and has the overall effect of adapting the hysteresis width. It is presented a formal proof that the proposed bimodal control leads to global stability without unwinding and is robust against chattering for any measurement noise with magnitude less than or equal to a given maximum value. Simulation results indicate that the proposed adaptive hysteresis width controller can be advantageous when the initial and final angular velocities have small magnitudes as is the case of the rest-to-rest attitude control problem.

Quaternion-based attitude synchronisation for multiple rigid bodies in the presence of actuator saturation

ABSTRACTThis paper concentrates on the quaternion-based attitude synchronisation problems of networked rigid bodies under fixed and undirected communication topology without relative angular measurements in the presence of actuator saturation. We first consider the leaderless attitude synchronisation problem with zero final angular velocity. In this case, we not only discuss the performance under the acyclic communication topology with the proposed bounded control algorithm, but also analyse that if there exist cycles in the topology, the proposed bounded algorithm guarantees that all equilibrium points are unstable except that the attitudes of networked rigid bodies achieve synchronisation. We also expand the result to the case of attitude tracking synchronisation with a static leader in the presence of actuator saturation. Next, the tracking synchronisation problem with the desired time-varying attitude is addressed in the presence of actuator saturation. Numerical examples are provided to validate the effectiveness of the proposed bounded schemes and illustrate the performances of multiple rigid bodies.

Models of cuspy triaxial stellar systems – IV. Rotating systems

We built two self-consistent models of triaxial, cuspy, rotating stellar systems adding rotation to non-rotating models presented in previous papers of this series. The final angular velocity of the material is not constant and varies with the distance to the center and with the height over the equator of the systems, but the figure rotation is very uniform in both cases. Even though the addition of rotation to the models modifies their original semiaxes ratios, the final rotating models are considerably flattened and triaxial. An analysis of the orbital content of the models shows that about two thirds of their orbits are chaotic yet the models are very stable over intervals of the order of one Hubble time. The bulk of regular orbits are short axis tubes, while long axis tubes are replaced by tubes whose axes lie on the short-long axes plane, but do not coincide with the major axis. Other types of regular orbits that do not appear in non-rotating systems, like horseshoes and orbits that cross themselves, are also found in the present models. Finally, our frequency maps show empty regions where studies of orbits on fixed potentials found orbits, a likely consequence of the self-consistency of our models that excludes them.

Radiation from an accelerating neutral body: The case of rotation

When an object is bound at rest to an attractional field, its rest mass (owing to the law of energy conservation, including the mass and energy equivalence of the Special Theory of Relativity) must decrease. The mass deficiency coming into play indicates a corresponding rest energy discharge. Thus, bringing an object to a rotational motion means that the energy transferred for this purpose serves to extract just as much rest mass (or similarly “rest energy”, were the speed of light in empty space taken to be unity) out of it. Here, it is shown that during angular acceleration, photons of fundamental energy \( h\varpi/2\pi\) are emitted, while the object is kept on being delivered to a more and more intense rotational accelerational field, \( \varpi\) being the instantaneous angular velocity of the rotating object. This fundamental energy, as seen, does not depend on anything else (such as the mass or charge of the object), and it is in harmony with Bohr’s Principle of Correspondence. This means at the same time, that emission will be achieved, as long as the angular velocity keeps on increasing, and will cease right after the object reaches a stationary rotational motion (a constant centrifugal acceleration), but if the object were brought to rotation in vacuum with no friction. By the same token, one can affirm that even the rotation at a macroscopic level is quantized, and can only take on “given angular velocities” (which can only be increased, bit by bit). The rate of emission of photons of concern is, on the other hand, proportional to the angular acceleration of the object, similarly to the derivative of the tangential acceleration with respect to time. It is thus constant for a “constant angular acceleration”, although the energy \( h\varpi/2\pi\) of the emitted photons will increase with increasing \( \varpi\) , until the rotation reaches a stationary level, after which we expect no emission --let us stress-- if the object is in rotation in vacuum, along with no whatsoever friction (such as the case of a rotating diatomic molecule, for instance). If the object reaches its final state in a given medium, say air, and “friction” is present, such as the case of a dental drill, then energy should keep being supplied to it, to overcome friction, which is present either inside the “inner mechanism of rotation” or in its surroundings. In other words, the object in the latter case, would be constantly subject to a friction force, countering its motion, and tending to make it fall to lower rotational energy states. Any fluctuations in the power supply, on the other hand, will slow down the rotating object, no matter how indiscernibly. The small decrease in the rotational velocity is yet reincreased by restoring the power supply, thus perpetually securing a stationary rotational motion. Thereby, the object in this final state, due to fluctuations in either friction or power supply, or both, shall further be expected to emit a radiation of energy \( h\varpi_{f}/2\pi\) , where \( \varpi_{f}\) is the final angular velocity of the object in rotation. What is more is that our team has very successfully measured what is predicted here, and they will report their experimental results in a subsequent article. The approach presented here seems to shed light on the mysterious sonoluminescence. It also triggers the possibility of sensing earthquakes due to radiation that should be emitted by the faults, on which the seismic stress keeps increasing until the crackdown. By the same token, also two colliding (neutral) objects are expected to emit radiation.

Attitude Synchronization for Multiple Rigid Bodies with Time Delays

In this paper we consider distributed attitude synchronization problem for multiple rigid bodies with time delays in the intercommunication. Based on graph theory and Lyapunov stability theory, we propose two distributed control laws. The first control law can guarantee attitude synchronization with zero final angular velocities when time delays exist. The second control law can guarantee attitude synchronization with non-zero final angular velocities when time delays exist. Throughout the paper, the communication flow among rigid bodies is assumed to be fixed and undirected.

Optimal Control of an Under-Actuated System for Landing With Desired Postures

Control over landing posture can effectively prevent structural damage when a portable device is accidentally dropped. Given size and cost constraints, the number of actuators should be limited. This paper presents an optimal posture control method that allows an under-actuated system to land with the desired posture. A simplified model of a portable computer/telephone is considered, comprising two rigid bodies and an active joint. The objective is to minimize the input torque produced by the actuator to achieve the desired posture. A two-point boundary value problem is formulated; i.e., the initial and final angular positions and velocities are predetermined, and the inequality constraints are established on the basis of the capacity of the actuator and acceptable level of state variables. In the numerical analysis, the backward-sweep algorithm is applied to determine the appropriate Lagrange multiplier, and the falling dynamics are explored using MATLAB. The optimal controller design is presented, together with simulation results confirming that the system is capable of performing landing posture control with minimum input torque.

Dynamic Contact Behavior of a Golf Ball during an Oblique Impact

The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images recorded before and after the impact were used to determine the inbound velocity vi, rebound velocity vr, inbound angle θi, rebound angle θr, and the coefficient of restitution e. The results showed that θr and e decreased as vi increased. The maximum compression ratio ηc, contact time tc, average angular velocity \(\overline{\omega } \), and tangential velocity \(\overline{v} _{{\text{t}}} \), along the target were determined from images obtained during the impact. The images demonstrated that ηc increased with vi while tc decreased. In addition, \(\overline{\omega } \) and \(\overline{v} _{{\text{t}}} \) increased almost linearly as vi increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity νt* at the end of the impact; these results were then compared with experimental data.

Oblique impact of inflated balls at large deflections

A planar theory for oblique impact of thin-walled spherical balls against a rough rigid surface has been developed on the basis of an assumed deformation field—an initially spherical ball is assumed to flatten against the constraint surface while the remainder of the ball remains undeformed. For inflated thin-walled balls, which are represented by these assumptions (basketballs, soccer balls, volleyballs, etc) the normal reaction force acting on the flattened contact patch is predominately due to the internal gas pressure—the reaction due to shell bending is insignificant in comparison with this gas force. During impact of a thin-walled ball there also is a non-conservative momentum flux reaction that is caused by the flow of momentum into and out-of the flattened contact patch. If the ball is translating as well as rotating about an axis perpendicular to the plane of motion, the distribution of the normal component of velocity for material entering and exiting the flattened contact patch results in a distribution of momentum flux force intensity around the periphery of the contact patch and consequently, a momentum flux torque acting on the flattened sphere. The effect of these reaction forces and torque on oblique impact of thin-walled spherical balls is calculated as a function of the ball deflection (or normal component of impact velocity). In comparison with rigid body calculations for oblique impact of a spinning ball against a rough surface at angles<45° from normal, the effect of maximum deflections as large as half the initial radius is to slightly accentuate the effect of friction on angle of rebound and moderately decrease the angular velocity of the ball. However, for angles >45° from normal, the final angular velocity can be as small as 40% of that predicted by rigid body theory. The most significant changes in rebound angle are for cases with initial backspin—a technique commonly used in many ball sports.

Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid**The project supported by National Natural Science Foundation of China under Grant Nos. 10347001, 70371067, and 10362001, the Key Technology Projects of the Ministry of Education of China under Grant No. 02115, and the Foundation of the Talent Project of Guangxi Province of China under Grant No.

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.

27S 軟式野球ボールの反発特性

The oblique impact of a rubber-ball for baseball with spin on a rigid plane surface is investigated using finite element analysis in order to utilize baseball bat design and obtain the common knowledge for the impact of many sorts of rubber-balls such as tennis ball. Parameters of a model are identified by the experiments and the analysis is performed precisely under the various conditions. It is found that restitution characteristics of the rubber-baseball are quantitatively different from but qualitatively similar to those of the tennis ball, the final angular velocity decreases under the constraint of ball slip at high incident velocity or by the reduction of gas pressure in the ball and the friction coefficient is identified effectively from the combination of the experiment and the analysis.

6S スピンを伴うテニスボールとラケットの衝突解析 : ボールのストリングス面への衝突解析

Although the role of ball-spin in tennis is extremely important, the phenomena of the impact with a spin seem difficult to understand. In order to make clear these phenomena, the numerical analysis programs based on finite element method have been developed. The oblique tennis-ball impact with spin on a clamped string face is investigated precisely using the computer simulation, to obtain the effect of strings in the impact on tennis racket. It is found that final angular velocity is higher than one in the case of the impact on a rigid plane surface and increases with initial ball velocity and the effect of initial string tension or impact location on the impact characteristics is small.

A new first integral for a binary rigid body collision of arbitrarily short duration

A standard classical model of a so-called rigid two-body collision that employs the dynamic Coulomb friction law to model friction is studied. For arbitrary object geometries and initial conditions it is known that the direction of the relative sliding velocity continuously changes during the impact. A (new) exact analytical solution for the relative sliding speed utr of the two objects in terms of initial conditions and sliding direction is derived. This solution is formulated in terms of a first integral, which is used to rigorously prove that the dynamic Coulomb friction law does not allow either instantaneous sticking or stable sticking to evolve from an initially nonzero utr, except for certain very special cases. The first integral also yields a new procedure for accurately and efficiently computing the final center of mass velocity and the final angular velocity of each of the objects in the model two-body collision. Accurate solutions such as these are essential for analyzing and controlling impacts, which is important, for example, in robot manipulation. Efficient solutions are critically important for producing real-time simulations of rigid two-body collisions.