Inertial Research Articles

Ellipsoidal estimation of motion parameters of a non-cooperative space vehicle from visual information

The use of near-Earth space is currently complicated by presence of space debris objects in Earth’s orbit, which include spent stages of launch vehicles, inoperative satellites, and other large and small artificial objects. One approach to solving the problem of space debris involves docking and capturing a non-cooperative space object or spacecraft (target) with a so-called service spacecraft (chaser) for further actions to repair, refuel or change its orbit. Rendezvous and docking are complicated by the rotation of uncontrolled space objects caused by various factors. To perform this task, it is necessary to know the parameters of the orbital, rotational and relative motion of the target. The parameters of the orbital motion of such objects are usually known quite accurately from measurements from the Earth. This paper examines the case of a tumbling non-cooperative target located in an elliptical orbit. It is assumed that the target relative position and orientation are measured by the computer vision system (CVS) of the chaser. In this case, the position and orientation of the graphical reference frame (GRF) associated with the known 3-D graphical model of the target are determined relative to the reference frame associated with the chaser. The specific type of CVS is not considered. It is assumed that the chaser can carry out some maneuvers near the target and all parameters of the chaser angular motion are known. Thus, the attitude of the GRF relative to inertial reference frame (IRF) can be determined. The measured parameters are not enough to ensure safe rendezvous and docking with the target. To complete this task, it is necessary to determine all kinematic and dynamic parameters of the relative motion between the spacecraft. The rest of the required parameters are estimated. Orientation and rotation parameterization is done using quaternions. The angular motion equation of the target is considered in the GRF. This makes the angular velocity estimation faster and the inertia tensor estimation more stable. Stochastic characteristics of measurement errors are considered to be unknown and are not used. The only information about the errors is the bounds of their values. To determine the relative motion parameters, we use a new dynamic set-membership filter with ellipsoidal estimates. The filter can be successfully implemented on low-power on-board processors. The properties of the proposed algorithm are demonstrated using numerical simulation. The results obtained are expected to be used in the development of a navigation system for the rendezvous and docking, developed by a group of Ukrainian space industry enterprises under the leadership of the LLC “Kurs-orbital” (https://kursorbital.com/).

Dynamic Analysis Strategy of Generalized Deployable Units via NCF-IGA with Force Constraint

Space deployable mechanisms typically employ modular designs, where each unit that can be independently deployed is defined as a generalized deployable unit (GDU), typically consisting of rigid components, flexible components and generalized kinematic pairs. Given the high-performance demands of spatial transmission mechanisms, generalized kinematic pairs frequently integrate flexible factors like torsion springs and flexible hinges, which control the motion according to the attitude and position of the component. In this investigation, a new modeling and solution strategy for rigid-flexible coupled dynamics is established by combining NCF and IGA. It can not only accurately describe the large deformation and large rotation of flexible components, but also consider the influence of flexible factors in the kinematic pairs. The rigid components are modeled by the Natural Coordinate Formula (NCF), and the flexible components are discretized in the inertial coordinate system using spline curves in Isogeometric Analysis (IGA). The intermediate reference coordinates were integrated into the NCF-IGA framework, overcoming the boundary constraints between B-spline and NCF elements, and the geometric constraint equation of the kinematic pair was established. Subsequently, this paper proposes the concept of force constraint in controllable deployable mechanisms. Based on the force constraint equation, the mechanical model of flexible joints is established. The dynamic equations of GDUs are derived considering both geometric and force constraints, and generalized-[Formula: see text] method is introduced to solve the equations. Finally, three numerical examples are provided to illustrate the applicability and superiority of the proposed method.

Analysis and suppression of the Rb resonance frequency error in NMR angular velocity sensor

The nuclear magnetic resonance (NMR) angular velocity sensor has the potential for high precision measurement in small volumes, which measures the 129Xe and 131Xe precession frequencies to obtain the angular velocity with respect to an inertial reference frame. One of the key challenges in frequency measurement is the long-term stability of the measured signal phase. The measured signal is acquired by applying a carrier magnetic field along the z-axis and demodulating the carrier signal at its frequency, which is typically fixed. However, fluctuations in light shifts and static magnetic fields can lead to instabilities in the Rb resonance frequency, consequently impacting the measurements of phase and precession frequencies of 129Xe and 131Xe. To address this issue, an analysis of the Rb resonance frequency error is conducted, and a suppression scheme based on carrier frequency correction is provided. This scheme can mitigate the effect of Rb resonance frequency fluctuations without further suppressing fluctuations of light shifts and static magnetic fields. The experiment demonstrates a 53.5 % reduction in the precession frequency error between 129Xe and 131Xe and a 59.0 % decrease in bias instability. This scheme can improve the long-term stability of 129Xe and 131Xe precession frequency measurements, thereby enhancing the performance of the NMR angular velocity sensor.

The length contraction paradox

Reciprocal length contraction and time dilation, as enshrined in the Lorentz transformation, are the bulwark of the special relativity theory. Reciprocal time dilation is typically discussed (in the context of its apparent contradiction) and usually explained away as the result of differing synchronization in inertial reference frames and the relativity of simultaneity. Further, it is generally suggested that time is an abstract concept, and its perceptions may differ with context. However, we suggest that regarding length measurements no such abstraction can be envisaged. In this manuscript, we examine the reciprocal length contraction in detail to assess whether it leads to any contradiction.

Theory of Everything

Our Theory of Everything is made possible by the discovery of a closed fluid dynamic principle, working in a closed fluid space-time system, (the universe). Through the principle of fluid space-time, almost all of the unexplained mysteries of the universe are revealed. How the universe came into being, with matter and the most basic force, Gravity. Newton’s law of gravity in particular, the inverse square law with distance. (the reason is for appearance of the inverse square law, simultaneously in gravitation and electromagnetism, not a coincidence). Special Relativity is an account of how space contracts, time dilates and mass increases, with velocity. General Relativity is an account of how space-time curves. According to Muhammad’s closed fluid dynamic principle, space actually consists of an extremely fluid substance which we call aether. It is therefore fitting that through the closed fluid dynamic principle, we can arrive at an explanation for one major thorn in the side of Special Relativity, the twin paradox. The problem is, it is the twin who accelerates that gets it wrong. Because his assessment of the age of his brother was done without consideration of the fact that when he turned around, made the return journey, he felt his acceleration but did not employ this in Einstein’s time dilation, which was based on inertial reference frames. The task we are confronted with in this paper is to find out how the time dilation addressed in special relativity comes into proceedings in an accelerated frame. We achieve this.

Model Establishment and Parameter Identification of Remotely Operated Vehicle (ROV)

Abstract To study the dynamic characteristics of remotely operated vehicle (ROV) underwater motion, a transformation matrix between the carrier coordinate system and the inertial coordinate system was established, and the rigid body dynamics model of the ROV was derived by using the Newton-Euler equation. According to the results of the ROV experimental prototype in this article, the dynamic model is simplified based on the force, motion characteristics, and structural characteristics. In the pool experiment, based on the propeller dynamic model, the least squares method was used to identify the parameters of the heading and vertical dynamic models, and through the experimental results under step control signals of different amplitudes, they were compared with the models under the same control signal. The output is subjected to error analysis. The experimental results show that the error between the theoretical value and the experimental value is small, verifying the accuracy of the ROV dynamics model established in this article.

Missing Data Filling of Model Based on Neural Network

Today’s society has entered the pace of information development era. All kinds of information are digitized, while the loss of information data also directly affects the normal operation of the application system and has become the biggest obstacle to the development of information technology. The existing missing filling methods do not take into account the time-series information of the data set. Based on the neural network method for filling missing data in time series, an end-to-end missing data filling method for time series based on the residual of regression equation is proposed. Under the assumption that the activation function and the noise diffusion coefficient function are satisfied, the exponential stability of the complex-valued stochastic inertial neural network systems with additive time-varying delays is studied. The bipartite graph model of the time series data missing value filling method of the countermeasure network and the filling cyclic neural unit are generated. According to the end-to-end time series data missing value filling method of the self encoder, the corresponding low-dimensional feature vector can be automatically generated for each time series data. It avoids overfitting by using nonlinear methods directly in low-dimensional space. Experiments show that the method proposed in this paper uses Monte Carlo to fill data missing at different proportions. In data gap filling process, the coefficient variance is less than 0.05, which enhances the rationality of filling data. It is of great research value and practical significance to reasonably fill in the missing values of time series data. The research can accelerate the improvement of big data system, improve the level and effectiveness of database management, and is an important means of computing capacity of existing data centers.

Third sound detectors in accelerated motion

An accelerated observer moving through empty space sees particles appearing and disappearing, while an observer with a constant velocity does not register any particles. This phenomenon, generally known as the Unruh effect, relies on an initial vacuum state, thereby unifying the experience of all inertial observers. We propose an experiment to probe this observer-dependent detector response, using a laser beam in circular motion as a local detector of superfluid helium-4 surface modes or third sound waves. To assess experimental feasibility, we develop a theoretical framework to include a non-zero temperature initial state. We find that an acceleration-dependent signal persists, independent of the initial temperature. By introducing a signal-to-noise measure we show that observing this signal is within experimental reach.

Point-charge models and averages for electromagnetic quantities considered in two relativistic inertial frames

Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather than point-charge distributions can lead to physically mystifying and even inaccurate results for electromagnetic quantities and physical phenomena. The discrepancy noted between the average electric field values in different inertial frames is particularly striking because it is first order in the relatative velocity between the frames.

Experimental Research on Shipborne SINS Rapid Mooring Alignment with Variance-Constraint Kalman Filter and GNSS Position Updates.

Analytical coarse alignment and Kalman filter fine alignment based on zero-velocity are typically used to obtain initial attitude for inertial navigation systems (SINS) on a static base. However, in the shipboard mooring state, the static observation condition is corrupted. This paper presents a rapid alignment method for SINS on swaying bases. The proposed method begins with a coarse alignment technique in the inertial frame to obtain an initial rough attitude. Subsequently, a Kalman filter with position updates is employed to estimate the remaining misalignment error. To enhance the filter estimation performance, an appropriate lower boundary is set to the target states' variances according to a carefully designed relative convergence index. The variance-constraint Kalman filter (VCKF) approach is proposed in this paper, and the shipborne experiments validate its effectiveness. The results demonstrate that the VCKF approach significantly reduces the time requirement for fine alignment to achieve the same accuracy on a swaying base, from 90 min in the classic Kalman filter to 30 min. Additionally, the parameter estimation performance in the Kalman filter is also improved, particularly in situations where unpredicted external interference is involved during fine alignment.

Dynamic modeling and parametric instability analysis of internally damped rotating composite shafts in inertial and rotating frames

Parametric resonance may occur when the composite shaft is subjected to periodic axial loads. The phenomenon will lead to the serious destruction of the dynamic system. In this study, we aim to investigate the parametric instability characteristics of rotating composite shafts considering internal damping, and to provide valuable theoretical guidelines for avoiding the occurrence of parametric resonance. The two dynamic models of the composite rotor in the inertial frame and rotating frame are both established using Hamilton's principle. The governing equations of the composite rotor are reduced into a system of Mathieu–Hill equations by means of the Galerkin method. Then Floquet exponent method is employed to conduct parametric stability analysis of the periodic loaded composite rotor. After performing validation of present model and method, numerical results are presented to bring out the influences of reference frame, rotation speed, internal damping and lamination angle on the parametric instability region. The results show that the selection of reference frame does not affect the determination of the size and type of the parametric instability region. However, it is more suitable to use the rotating frame from the perspective of determining the type of the unstable region. The internal damping of composites should not be ignored when analyzing the parametric stability of composite rotors, especially for the high order excitation frequency.

Validation of Inertial-Measurement-Unit-Based Ex Vivo Knee Kinematics during a Loaded Squat before and after Reference-Frame-Orientation Optimisation.

Recently, inertial measurement units have been gaining popularity as a potential alternative to optical motion capture systems in the analysis of joint kinematics. In a previous study, the accuracy of knee joint angles calculated from inertial data and an extended Kalman filter and smoother algorithm was tested using ground truth data originating from a joint simulator guided by fluoroscopy-based signals. Although high levels of accuracy were achieved, the experimental setup leveraged multiple iterations of the same movement pattern and an absence of soft tissue artefacts. Here, the algorithm is tested against an optical marker-based system in a more challenging setting, with single iterations of a loaded squat cycle simulated on seven cadaveric specimens on a force-controlled knee rig. Prior to the optimisation of local coordinate systems using the REference FRame Alignment MEthod (REFRAME) to account for the effect of differences in local reference frame orientation, root-mean-square errors between the kinematic signals of the inertial and optical systems were as high as 3.8° ± 3.5° for flexion/extension, 20.4° ± 10.0° for abduction/adduction and 8.6° ± 5.7° for external/internal rotation. After REFRAME implementation, however, average root-mean-square errors decreased to 0.9° ± 0.4° and to 1.5° ± 0.7° for abduction/adduction and for external/internal rotation, respectively, with a slight increase to 4.2° ± 3.6° for flexion/extension. While these results demonstrate promising potential in the approach's ability to estimate knee joint angles during a single loaded squat cycle, they highlight the limiting effects that a reduced number of iterations and the lack of a reliable consistent reference pose inflicts on the sensor fusion algorithm's performance. They similarly stress the importance of adapting underlying assumptions and correctly tuning filter parameters to ensure satisfactory performance. More importantly, our findings emphasise the notable impact that properly aligning reference-frame orientations before comparing joint kinematics can have on results and the conclusions derived from them.

Gait Characteristics over the Six-minute Walk Test in Older Women of a Specific Portuguese Community: A Cross-Sectional Study.

There is limited research on the changes that can occur in the gait biomechanical parameters of older adults over long-distance walking. Thus, this study aimed to evaluate the gait characteristics of older women of a specific Portuguese community over the six-minute walk test (6MWT) along with gait spatial and temporal parameters and angular kinematics of the lower limb joints. Twenty-six older women voluntarily participated. Each woman performed the 6MWT, and during this, their spatial and temporal parameters were collected through plantar pressure data (100Hz) and angular kinematics through an inertial sensor system (100Hz). The 6MWT was divided into four intervals, and the Friedman test was used to compare them. The median age of the women was calculated, and the Mann-Whitney test was used to compare women above and below the median age value. An increase in gait speed, stance phase, and double stance phase along the intervals was observed, as well as larger angular displacements of the hip, knee, and ankle (p<0.05). Women below or above the median age value also yielded these behaviours. Gait speed, cadence, stride length, and step length were higher in women below the median age value, while stride and step duration were lower (p<0.05). Older women yielded changes in gait spatial and temporal parameters along the 6MWT, as well as larger angular displacements of the lower limb joints. Older women (compared to younger ones) yielded lower gait speed, cadence, stride length, and step length, higher stance and double stance phases, and shorter angular displacements of the lower limb joints.

On the radiation field of a linearly accelerated charged particle in Born–Infeld theory

The electric potential and the electromagnetic field for a linearly accelerated Born–Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based on (i) the fact that the metric near the horizon of a Schwarzschild black hole is equivalent to that of Rindler spacetime, and (ii) a theorem that guarantees that the electrostatic potential for a given nonlinear theory in a static, spherically symmetric spacetime is entirely specified by the Maxwellian electrostatic potential in the same background. Using analytical and numerical methods, the features of the radiation field and the radiation-reaction for such an accelerated particle are discussed in detail.

Three-Body 3D-Kepler Electromagnetic Problem—Existence of Periodic Solutions

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld’s hypothesis for the He atom.

Biceps femoris muscle-tendon strain during an entire overground sprint acceleration: a biomechanical explanation for hamstring injuries in the acceleration phase

ABSTRACT The objectives of this study were to analyse the peak muscle-tendon (MT) strain of the hamstring during an entire acceleration sprint overground and examine their relationship with relative joint angles and segment orientation in the sagittal plane, which are the direct causes of MT strain. Kinematic data were recorded using a 3D inertial motion capture system in 21 male semi-professional soccer players during 40-metre overground sprint. Scaled musculoskeletal models were used to estimate peak MT strain in the hamstring over 16 steps. Biceps femoris long head (BFLH) exhibited the largest peaks in MT strain compared to semitendinosus (ST) and semimembranosus (SM) muscles across all the steps, with its overall strain decreased as the number of steps and maximum speed increased. Hip flexion angle was found to be a strong predictor (p < 0.001) of joint angles, being the orientation of the pelvis in the sagittal plane of the segment with the greatest influence (p < 0.001) on the peak MT strain of BFLH during sprinting. The current study provides a biomechanical explanation for the high proportion of hamstring injuries in the acceleration phase of sprinting.

SPECIAL THEORY OF RELATIVITY IS ALSO FAILED TO EXPLAIN NULL RESULT OF MICHELSON AND MORLEY EXPERIMENT

Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether. In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference fringes. Keeping in view known velocity of earth around the sun a fringe shift of 0.44 fringe was expected on the rotation of interferometer at an angle of 900, but surprisingly no fringe shift was observed. The experiment was conducted so many times and at so many places but always null results were obtained. The null result of MMX could not be explained by classical mechanics. A number of explanations for null results were submitted but no one was found to be correct. George Fitzerald and Hendrick Lorentz proposed length contraction hypothesis in the direction of motion of earth, but it was also rejected being an adhoc hypothesis. Albert Einstein submitted his famous theory “The special theory of relativity” in the year 1905. The second postulate of the STR states that speed of light is constant in all directions of inertial frames of reference irrespective of motion of source of light or the observer and states that no luminiferous aether exist as a medium, light waves do not require any medium to propagate. As light travels with constant velocity in both the arms of interferometer irrespective of motion of interferometer and there involves no time difference between the two rays hence null results of MMX were explained by special theory of relativity. Michelson and Morley experiment is based on the wave nature of light. In such experiments wavefront of light plays very important role but behaviour of wavefront of light was not taken into consideration while deriving the time taken by the light rays in the arms of interferometer due to motion of earth resulting into wrong derivation of time. The present article describes the principle and realization of role of wavefront of light in MMX. The time taken by light rays in the arms of the interferometer due to motion of earth depends upon the behaviour of wavefront of light. It has been established by results of Fizeau experiment and steller aberration of light that speed of light is not effected by velocity of moving medium. The derivation of time has been worked out keeping in view constancy of speed of light, wavefront of light and laws of reflection of light according to Huygen’s principle. Contrary to earlier beliefs the Lorentz length contraction hypothesis is not able to explain the null results of MMX. In the light of new facts it is established that there is no difference between theorectical results derived by classical mechanics and special theory of relativity. Special theory of relativity is also failed to explain the null result of MMX. The null result of Michelson and Morley experiment has again become a perplexing question for physicists.

Integration of Sonar and Visual–Inertial Systems for SLAM in Underwater Environments

Integration of Sonar and Visual–Inertial Systems for SLAM in Underwater Environments

Optimal orbit transfer of single-tether E-sail with inertially fixed spin axis

This study analyzes the optimal transfer trajectory of a spacecraft propelled by a spin-stabilized electric solar wind sail (E-sail) with a single conducting tether and a spin axis with a fixed direction in an inertial (heliocentric) reference frame. The approach proposed in this study is useful for rapidly analyzing the optimal transfer trajectories of the current generation of small spacecraft designed to obtain in-situ evidence of the E-sail propulsion concept. In this context, starting with the recently proposed thrust model for a single-tether E-sail, this study discusses the optimal control law and performance in a typical two-dimensional interplanetary transfer by considering the (binary) state of the onboard electron emitter as the single control parameter. The resulting spacecraft heliocentric trajectory is a succession of Keplerian arcs alternated with propelled arcs, that is, the phases in which the electron emitter is switched on. In particular, numerical simulations demonstrated that a single-tether E-sail with an inertially fixed spin axis can perform a classical mission scenario as a circle-to-circle two-dimensional transfer by suitably varying a single control parameter.

Multiple scroll attractors and multistability in the collective dynamics of a four chain coupled hopfield inertial neuron network: analysis and circuit design investigations

This work deals with the chain bidirectional coupling of four inertial Hopfield neurons. Each of our cells taken alone is modeled by a second order differential equation having three resting points. Coupling these neurons helps increasing the number of fixed points that is related to the amount of memory assigned to the network. The system having a hyperbolic tangent as nonlinearity is investigated with the help of suitable nonlinear dynamical tools like bifurcation diagrams, Lyapunov exponent diagrams and phase portraits to resort the richness of the model. As the coupling adds the amount of equilibriums, it also helps in generating multiple scroll attractors. The system that was unable of oscillation presents firing patterns such as parallel branches, coexistence of up to sixteen attractors in the phase plane, extreme events and Hopf bifurcation to name a few. All these features are discovered when observing the coupling strengths, the dissipation coefficient and when programming initial states around sensitive equilibriums. The electronic version of the four-chain coupled inertial neurons system is provided and simulated on Pspice with the aim to confirm the results obtained in the numerical scheme.