Search

With the rapid development of remote sensing imaging and deep learning technology, the fine-grained recognition of rigid targets has gradually emerged. Rigid targets in remote sensing scenes usually retain relatively stable scale information and apparent structure, providing an adequate basis for their discrimination. However, existing methods need to more reasonably utilize the scale information and apparent structure, which results in scale neglect and insufficient discriminative feature extraction (DFE). In response to the aforementioned challenges, we propose our SD-Net, a training framework for fine-grained recognition tasks of rigid objects in remote sensing scenes. It consists of a fused label learning process based on probability distribution function (PDF) and a DFE branch. The PDF counts the objects' scale information by category, builds a probability model based on the sample distribution, and finally converts it into a soft label form to guide model learning. DFE extracts discriminative features along the channel and spatial dimensions of the feature map based on feature deep mining and wide-ranging. Finally, we propose the FAIR1M-OR dataset, containing 37 fine-grained categories and about 600 000 instances, to verify the method's effectiveness. The experimental results show that introducing only a small number of parameters during training, SD-Net, improves the performance of the models based on the ResNet and ViT by about 4.6 points. The code and dataset will be open source in the future.

Abstract This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.

The problem of tracking control is addressed for rigid bodies with interior shallow-water sloshing. The liquid motion is modeled by the Saint-Venant equations, coupled with the ODE of the rigid body, leading to a global system with an ODE-hyperbolic PDE cascade structure. The paper aims to design an innovative boundary feedback framework for a pre-specified position to deal with rigid body tracking errors. Using only one control force applied to the rigid body, the formulated strategy efficiently stabilizes both the finite- and infinite-dimensional states. The main complexity lies in the fact that no sensor can be implemented in the liquid domain. Indeed, the proposed stabilizing feedback law simply requires measurements of (i) the rigid body position error and velocity and (ii) the liquid pressure at the cavity walls (liquid boundary). The asymptotic stability of the closed-loop system is analyzed using the Lyapunov direct method and LaSalle’s invariance principle without any discretization, reduction, and linearization. Additional controller features are highlighted by simulation results, including its benefits in contrast to the corresponding PD controller and its robustness to time delay and system uncertainty.

The problem of tracking control is addressed for rigid bodies with interior shallow-water sloshing. The liquid motion is modeled by the Saint-Venant equations, coupled with the ODE of the rigid body, leading to a global system with an ODE-hyperbolic PDE cascade structure. The paper aims to design an innovative boundary feedback framework for a pre-specified position to deal with rigid body tracking errors. Using only one control force applied to the rigid body, the formulated strategy efficiently stabilizes both the finite- and infinite-dimensional states. The main complexity lies in the fact that no sensor can be implemented in the liquid domain. Indeed, the proposed stabilizing feedback law simply requires measurements of (i) the rigid body position error and velocity and (ii) the liquid pressure at the cavity walls (liquid boundary). The asymptotic stability of the closed-loop system is analyzed using the Lyapunov direct method and LaSalle’s invariance principle without any discretization, reduction, and linearization. Additional controller features are highlighted by simulation results, including its benefits in contrast to the corresponding PD controller and its robustness to time delay and system uncertainty.

This study delves into moment of inertia in rigid body mechanics, a crucial concept in physics. While it’s traditionally taught through integration, we propose an alternative method using discrete mass segments. This approach simplifies calculations, particularly for symmetric bodies, without complex integration procedures. Our goal is to enhance students’ understanding of fundamental physics principles, making the subject more accessible. We also provide visual aids and online animations to aid comprehension.

Computational fluid dynamics has been widely used in the design and analysis of various fluid systems. The proper treatment of boundary conditions is crucial for the accurate simulation of fluid flow. However, in particle methods, such as smoothed particle hydrodynamics method and moving particle semi-implicit method, the treatment of boundary conditions has been a challenging problem. In this paper, starting from the incompressibility condition, we present a new theory for the unified treatment of both rigid bodies and wall boundaries, which allows the strong coupling of rigid bodies and incompressible fluids. Because the boundary models are based on signed distance functions and do not use particles, these models can avoid several problems, such as resolution dependence of particle representations, and unavoidable unevenness of surfaces. We also provide a way to efficiently handle rigid-body boundaries and wall boundaries without particles by finding the fundamental boundary weight function that does not change with time. Several numerical examples are presented to demonstrate the capability of our models and to compare them with theoretical and experimental results.

Abstract In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A $\mathcal{A}$ of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.

Perturbed motions of a rigid body, close to the Lagrange case, under the action of restoring and perturbation torques of forces are investigated in the paper. The following problem is formulated: investigating solutions behavior of system of equations of motion for nonzero values of small parameter on a sufficiently long time interval. To analyze a nonlinear system of equations of motion, the averaging method is used. The problem can be decomposed into slowly and quickly changing variables. Conditions for the possibility of averaging the equations of motion with respect to the phase of nutation angle are presented and averaging procedure for slow variables of a perturbed motion of a rigid body in the first approximation is described. As an example of the developed procedure, we investigate a perturbed motion, close to Lagrange case, taking into account constant dissipative and small torque, and dissipative torques depending on slow time. A new class of rotational motions of a dynamically symmetric rigid body about a fixed point has been investigated with restoring and perturbation torques of forces being taken into account.

Ship resistance is an important characteristic to predict in the preliminary design stage. Proper prediction of ship resistance implies the fulfillment of the required speed and power of a ship. The assumed body characteristics of a ship model should also be properly considered when investigating ship resistance. In the present study, the assumption of a hydroelastic body for a ship model was used in an experiment on total ship resistance and added resistance in calm water and waves. Two hydroelastic models were used: a hydroelastic body with a bulbous bow (HB) and a hydroelastic body without a bulbous bow (HWB). The wavelength considered ranged from 0.5 L to 1.3 L, and the Froude number (Fn) considered ranged from 0.058 to 0.232. In the presented results, the total resistance coefficient of the HWB was higher than that of a rigid body without a bulbous bow (RWB). The average difference of magnitude between the HWB and RWB was 30.49% for calm water conditions and 30.37% for overall wave conditions. The total resistance of the HB was higher than that of the rigid body with a bulbous bow (RB), and the difference of magnitude was approximately 31.47% for calm water conditions and 31.68% for overall wave conditions. The added resistance coefficient of the HWB tended to increase with an increase in the wavelength, from 0.5 L to 1.1 L, and then decrease until 1.5 L. The overall tendency of the added resistance coefficient of the HB was significantly different from the other numerical results. Although the tendencies were different, most of the presented results were in the same range as the other numerical results.

The primary goal of this project was to develop a general identification method via software that can be applied to collaborative robots. To achieve this, the collaborative ultralight robots Kinova Gen2 and Kuka LWR4+ with seven degrees of freedom (M-DOF) were used. Specifically, the “recursive Newton-Euler” formulation was used to provide a set of parameters that could describe the body structure and to create a general symbolic representation for collaborative robots. For parameter estimation, the least squares method was used. In addition, trajectories generated with random numbers typically do not produce consistent results; thus, verified trajectories were used. To verify trajectories, real robots were simulated with V-Rep before being executed. When untested trajectories are first tested on robots, undesirable results may occur. This method was convenient for parameter estimation and robot health; saves time; and increases the consistency of results. Algorithms were coded in MATLAB and ROS packages via Python. MATLAB, ROS, and V-Rep worked together in the Ubuntu operating system. The identification methods were modeled, implemented, tested, and validated successfully, and the results for both robots are reported in this article.

This study investigates the challenging and complicated issue of full-state constraint attitude control for rigid bodies under actuators physical limitation. Using the concept of prescribed performance control (PPC), a novel proportional-derivative (PD)-type control is introduced by which both the attitude quaternion and the rotation velocity of the rigid body are enforced to possess specific behaviors in transient and steady state. To this end, a prescribed performance function (PPF) with finite-time convergence is first defined as the predefined boundaries for the quaternion and rotation velocity. Subsequently, a constrained PD-type attitude control for rigid body attitude system is developed. The significant difference between the proposed methodology and the PPC is the simple structure of the controller making it more applicable from practical implementation point of view. Indeed, due to the use of error transformation in the PPC, the controller contains partial derivative terms and complicated functions even for only constraining the attitude quaternion. When it comes to angular velocity constraint as well, the complexity of the control design procedure is doubled. It is rigorously proved that the suggested control framework can successfully satisfy constraints not only on the quaternion but also on the angular velocity, simultaneously. These interesting results are obtained even when the actuator saturation is considered. The simulation results conducted on a rigid spacecraft verify the efficacy and applicability of the suggested constrained attitude control approach.

In this paper, we propose a geometric control law for attitude robust control problem of a rigid body system without angular velocity measurement. We suppose there is a disturbance related to angular velocity and attitude in the system. Under appropriate controllers, the estimated values of attitude and angular velocity obtained by an angular velocity observer can converge to the true values exponentially by the Lyapunov stability theorem. Furthermore, by modifying an adaptive law for the inertia matrix, the exponential stabilization of the system can still be guaranteed without the knowledge of the true inertia matrix with the same way. The angular velocity observer we designed ensures the global exponential stability in the system. Finally, the proposed theoretical results are verified by our simulation examples.

Abstract Background To report prostate deformation during treatment, based on an analysis of fiducial marker positional differences in a large sample. Material and methods This study included 144 patients treated with prostate stereotactic body radiation therapy after implantation in each of 4 gold fiducial markers (FMs), which were located and numbered consistently. The center of mass of the FMs was recorded for every pair of X-ray images taken during treatment. The distance between each pair of fiducials in the live X-ray images is calculated and compared with the respective distances as determined in the CT volume. The RBE is the difference between these distances. Mean RBE and intrafraction and interfraction RBE were evaluated. The intrafraction and intefraction RBE variability were defined as the standard deviation, respectively, of all RBE during 1 treatment fraction and of the mean daily RBE over the whole treatment course. Results We analyzed 720 treatment fractions comprising 24,453 orthogonal X-ray image acquisitions. We observed a trend to higher RBE related to FM4 (apex) during treatment. The fiducial marker in the prostate apex could not be used in 16% of observations, in which RBE was > 2.5 mm. The mean RBEavg was 0.93 ± 0.39 mm (range 0.32–1.79 mm) over the 5 fractions. The RBEavg was significantly lower for the first and second fraction compared with the others (P

To verify the dynamic model of a paddy-field laser grader and solve the problem of the unstable high-speed operation of the grader, a method for measuring the absolute pose parameters of a moving rigid body using a monocular camera is proposed. The proposed method does not require calibration beforehand. Using more than six non-coplanar control points symmetrically arranged in the rigid-body and world coordinate systems, the matrices of rotation and translation between the camera and two coordinate systems are obtained and the absolute pose of the rigid body is measured. In this paper, formulas of the absolute pose measurement of a moving rigid body are deduced systematically and the complete implementation is presented. Position and attitude measurement experiments carried out on a three-axis precision turntable show that the average absolute error in the attitude angle of a moving rigid body measured by an uncalibrated camera at different positions changes by no more than 0.2 degrees. An analysis of the three-dimensional coordinate errors of the centroid of a moving rigid body shows little deviation in measurements taken at the three camera positions, with the maximum deviation of the average absolute error being 0.53 cm and the maximum deviation of the standard deviation being 0.66 cm. The proposed method can measure the absolute pose of a rigid body and is insensitive to the position of the camera in the measurement process. This work thus provides guidance for the repeated measurement of the absolute pose of a moving rigid body using a monocular camera.

Background and purpose: Surface guided radiotherapy can be used to improve patient setup and for accurate intra-fraction motion monitoring in correspondence to the isocenter. For a clinical relevant motion analysis the actual displacement of the entire clinical target volume (CTV) is necessary. Therefore, the aim of this study was to develop a novel assessment method for intra-fraction motion for rigid body structures based on motion data and a geometrical analysis. Materials and methods: A threshold value on the volume coverage (VC(t)) of the CTV by the planning target volume (PTV) was proposed as online motion monitoring method. Moreover, offline analysis was performed by using heat maps and by calculating VCx, the volume coverage for at least x% of treatment time. The method was applied retrospectively to patient treatment data for whole brain radiation treatment without a thermoplastic mask. Results: In 132 out of 142 fractions in total the proportion of the CTV that was inside the PTV for at least 99% of the time (VC99) was more than 95%, for a CTV-to-PTV margin of 5 mm. The source-voxel heat map showed which part of the CTV had a reduced coverage and the target heat map showed the movement of the CTV. Conclusion: Instead of using an action threshold on the movements of the isocenter, a threshold on the VC(t) of the CTV by the PTV was proposed. The heat maps and resulting values of VCx can be used to adapt the VC(t) threshold or the CTV-to-PTV margin for subsequent fractions.

A rigid body forced by a nonstationary perturbing torque with zero mean value is under consideration. The control strategy for attitude stabilization of the rigid body is based on the usage of dissipative and restoring torques. It is assumed that the dissipative torque is linear, while restoring and perturbing torques are purely nonlinear. A theorem on sufficient conditions for asymptotic stability of the body angular position is proved on the basis of the decomposition method, the Lyapunov direct method and the averaging technique. Computer simulation results illustrating the theorem are presented.

We consider the linearized and nonlinear systems describing the motion of incompressible flow around a rotating and translating rigid body Ɗ in the exterior domain Ω = ℝ3 \ Ɗ, where Ɗ ⊂ ℝ3 is open and bounded, with Lipschitz boundary. We derive the L∞-estimates for the pressure and investigate the leading term for the velocity and its gradient. Moreover, we show that the velocity essentially behaves near the infinity as a constant times the first column of the fundamental solution of the Oseen system. Finally, we consider the Oseen problem in a bounded domain ΩR := BR ∩ Ω under certain artificial boundary conditions on the truncating boundary ∂BR, and then we compare this solution with the solution in the exterior domain Ω to get the truncation error estimate.

Abstract Relationship between contact size (A) and static friction (f) has been studied for rigid crystalline systems. We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction. In these systems, there are numerous nontrivial commensurate contacts. Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact. For commensurate contacts, f ∝ A independent of the shape. For incommensurate contacts, generally f ∝ A 0 for regular shapes or f ∝ A 1/4 for irregular shapes; however, in very few cases of regular shapes, f ∝ A 1/2. Moreover, in above systems, commensurability of a contact can be easily changed by a perturbation of the misfit angle. Therefore, if the perturbation caused by the lateral force and the deformation of the surface are considered (as is the case in real systems), further research is necessary.

The pendulum's motion better understanding enhances the researcher's ability to solve many engineering challenges. This article explores the motion of three-degrees-of-freedom nonlinear dynamic mechanism described by a damped rigid body pendulum in which its suspended point travels along the Lissajous trajectory. In light of this system's generalized coordinates, we used Lagrange's equations to derive the governing system of motion. The asymptotic solutions of the equations of this system up to the third approximation are obtained using the multiple scale technique. The resonance cases are classified and the conditions of solvability are examined in view of the modulation equations in which the steady-state solutions are verified. The stability criteria were carried out in addition to simulations of the evolution of the non-linear equations of the considered system using the approach of nonlinear stability analysis. The time history of the considered motion, the resonance curves and steady-state solutions are graphically presented in accordance with the effect of various physical parameters on the motion. The numerical results of governing system are obtained using the fourth-order Runge–Kutta algorithms and compared with the asymptotic ones to reveal the high consistency between them and to clarify the accuracy of the used perturbation technique.

Damping is an important factor contributing to errors in the measurement of rotational inertia using the torsion pendulum method. Identifying the system damping allows for minimizing the measurement errors of rotational inertia, and accurate continuous sampling of torsional vibration angular displacement is the key to realizing system damping identification. To address this issue, this paper proposes a novel method for measuring the rotational inertia of rigid bodies based on monocular vision and the torsion pendulum method. In this study, a mathematical model of torsional oscillation under a linear damping condition is established, and an analytical relationship between the damping coefficient, torsional period, and measured rotational inertia is obtained. A high-speed industrial camera is used to continuously photograph the markers on a torsion vibration motion test bench. After several data processing steps, including image preprocessing, edge detection, and feature extraction, with the aid of a geometric model of the imaging system, the angular displacement of each frame of the image corresponding to the torsion vibration motion is calculated. From the characteristic points on the angular displacement curve, the period and amplitude modulation parameters of the torsion vibration motion can be obtained, and finally the rotational inertia of the load can be derived. The experimental results demonstrate that the proposed method and system described in this paper can achieve accurate measurements of the rotational inertia of objects. Within the range of 0–100 × 10−3 kg·m2, the standard deviation of the measurements is better than 0.90 × 10−4 kg·m2, and the absolute value of the measurement error is less than 2.00 × 10−4 kg·m2. Compared to conventional torsion pendulum methods, the proposed method effectively identifies damping using machine vision, thereby significantly reducing measurement errors caused by damping. The system has a simple structure, low cost, and promising prospects for practical applications.

The study of the motion of a rigid body on a plane (RBP motion) is usually one of the most challenging topics that students face in introductory physics courses. In this paper, we discuss a couple of problems which are typically used in basic physics courses, in order to highlight some aspects related to RBP motion which are not usually well understood by physics students. The first problem is a pendulum composed of a rod and disk. The angular frequency of the pendulum is calculated in two situations: disk fixed to the rod and disk free to spin. A detailed explanation of the change in the angular frequency from one case to another is given. The second problem is a ladder which slides touching a frictionless surface. We use this problem to highlight the fact that the contact forces applied by the surface perform translational and rotational work despite that the total mechanical energy of the ladder is conserved.

This paper investigates the motion of a dynamically symmetric rigid body about one of its fixed points in which it is incurred to Newtonian force field, electromagnetic field and external torques. These torques acted in the direction of the principal axes of the body and are represented by perturbing and gyrostatic torques. The body rotates initially about the symmetry dynamic axis with high angular velocity. Therefore, a small parameter can be introduced. The averaging method is applied to convert the governing system of motion into another convenient averaging one in terms of a small parameter. The asymptotic analytical solutions of the latter system are obtained for some distinct applications depending upon the perturbing torques and the restoring one. The good effect of the body parameters on the motion is clarified in the graphical representations of the obtained solutions of the considered applications. The significance of this work is due to its great implementation of practical life like submarines, devices that maintain the stability and measure the orientations of airplanes and for several physics and engineering applications.

Abstract Background Results of finite element (FE) analyses can give insight into musculoskeletal diseases if physiological boundary conditions, which include the muscle forces during specific activities of daily life, are considered in the FE modelling. So far, many simplifications of the boundary conditions are currently made. This study presents an approach for FE modelling of the lower limb for which muscle forces were included. Methods The stance phase of normal gait was simulated. Muscle forces were calculated using a musculoskeletal rigid body (RB) model of the human body, and were subsequently applied to a FE model of the lower limb. It was shown that the inertial forces are negligible during the stance phase of normal gait. The contact surfaces between the parts within the knee were modelled as bonded. Weak springs were attached to the distal tibia for numerical reasons. Results Hip joint reaction forces from the RB model and those from the FE model were similar in magnitude with relative differences less than 16%. The forces of the weak spring were negligible compared to the applied muscle forces. The maximal strain was 0.23% in the proximal region of the femoral diaphysis and 1.7% in the contact zone between the tibia and the fibula. Conclusions The presented approach based on FE modelling by including muscle forces from inverse dynamic analysis of musculoskeletal RB model can be used to perform analyses of the lower limb with very realistic boundary conditions. In the present form, this model can be used to better understand the loading, stresses and strains of bones in the knee area and hence to analyse osteotomy fixation devices.

A weakly compressible SPH (WCSPH) scheme has been developed to simulate interaction between waves and rigid bodies. The developed WCSPH scheme is improved by applying a modified equation to calculate the wave-structure interaction, in order to increase its accuracy. The effects of relative fluid/solid particles’ acceleration are considered in the modified equation. To evaluate the efficiency of developed model, the dynamics of structural movements and related pressure fields are investigated for several test cases and the results are compared with the experimental data. It seems that the modified algorithm is able to improve the accuracy of simulated wave-structure interactions.

We show that a heavy, magnetized and electrically charged asymmetric rigid body moving about a fixed point while carrying a rotor and acted upon by three uniform fields can perform a regular precession about a nonvertical axis, of the type described for the case of a single field by Grioli in 1947. This is the first, and the only known by now, non-equilibrium solution of the problem of motion of a body in the presence of three classical fields, which are irreducible to a less number of fields.

Abstract: This study aims to determine the relationship between students mastery of concepts and problem solving on the rigid body lesson. This research was a correlational study. The research sample consisted of 64 students of 12th class of the state senior high schools were selected using purposive random sampling. The research instrument consisted of multiple choice questions to measure students ‘mastery of concepts and problem descriptions to measure students’ problem-solving. The average value of students’ mastery of concepts and problem solving students respectively were 52.81 (11.98) and 31.95 (10.06). Data results of both tests were analyzed with Pearson product moment correlation. The results showed a positive correlation between mastery of concepts to problem-solving student. Key Words: mastery of concepts, problem solving, rigid body Abstrak: Penelitian bertujuan untuk mengetahui hubungan antara penguasaan konsep dan pemecahan masalah siswa pada materi benda tegar. Jenis penelitian adalah penelitian korelasional. Sampel penelitian terdiri dari 64 siswa kelas XII dari dua sekolah SMA Negeri yang dipilih menggunakan purposive random sampling. Instrument terdiri dari soal pilihan ganda untuk mengukur penguasaan konsep dan uraian untuk mengukur pemecahan masalah. Rata-rata nilai penguasaan konsep dan pemecahan masalah berturut-turut adalah 52,81(11,98) dan 31,95(10,06). Data hasil kedua tes dianalisis dengan korelasi pearson product moment. Hasil penelitian menunjukkan adanya korelasi positif antara penguasaan konsep dengan pemecahan masalah siswa. Kata kunci: penguasaan konsep, pemecahan masalah, benda tegar

In order to investigate the seismic performance of prestressed concrete rocking frame (PCRF), a theoretical model based on rigid body is established for a one-story single-span PCRF. The PCRF studied in this paper has the connecting interfaces set at the column feet and at the inner faces of the beam–column joints, allowing the columns to be uplifted with the accompanying separation of the beam–column interface and rotation of the beam and column around the interface. The tendons are arranged along the centerline of the beam and columns. The connections between the beam and columns and the anchoring of columns are accomplished by prestressing the tendons. The theoretical model consists of a rigid beam, rigid columns and elastic tendons. The governing motion equation of the PCRF is derived based on the model and a numerical solution of the equation of motion is obtained. The energy dissipation of the PCRF is analyzed and the calculation method for the coefficient of restitution is derived. Time history analysis and parameter analysis of seismic response of the PCRF are conducted and the results show that the PCRF has promising seismic behavior.

The measurement of six-degrees-of-freedom (6-DOF) of rigid bodies plays an important role in many industries, but it often requires the use of professional instruments and software, or has limitations on the shape of measured objects. In this paper, a 6-DOF measurement method based on multi-camera is proposed, which is accomplished using at least two ordinary cameras and is made available for most morphological rigid bodies. First, multi-camera calibration based on Zhang Zhengyou’s calibration method is introduced. In addition to the intrinsic and extrinsic parameters of cameras, the pose relationship between the camera coordinate system and the world coordinate system can also be obtained. Secondly, the 6-DOF calculation model of proposed method is gradually analyzed by the matrix analysis method. With the help of control points arranged on the rigid body, the 6-DOF of the rigid body can be calculated by the least square method. Finally, the Phantom 3D high-speed photogrammetry system (P3HPS) with an accuracy of 0.1 mm/m was used to evaluate this method. The experiment results show that the average error of the rotational degrees of freedom (DOF) measurement is less than 1.1 deg, and the average error of the movement DOF measurement is less than 0.007 m. In conclusion, the accuracy of the proposed method meets the requirements.

This paper presents a dynamic simulation technique for the rigid body system coupled with the hydraulic system considering the digging behavior of the soil. The rigid body system and hydraulic system is modeled based on the Newton-Euler formulation, while the soil is modeled by the discrete element method (DEM) using the cohesive model proposed by Utili and Nova(2008). The co-simulation is carried out for the rigid body/hydraulic coupling system and the soil. Firstly, the digging simulation of the soil for the bucket of the hydraulic excavator is carried out for the cohesive soil and the sandy soil. The digging behavior of the soil and the digging force are discussed. Secondly, the co-simulation technique for the rigid body/hydraulic coupling system and the soil is presented. Finally, the dynamic simulation of the hydraulic excavator is carried out for the digging operation, the behavior of the hydraulic system and the soil is discussed for the cohesive soil and the sandy soil. It is shown that the digging power of the arm driving system for the sandy soil can be reduced by considering the cohesive force. It is clarified that the present technique can evaluate the hydraulic system of the hydraulic excavator for any characteristics of the soil.

In this paper, I present an overview of the active area of interactions between algebraic geometry and algebraic completely integrable systems. These are integrable systems whose trajectories are straight line motions on complex algebraic tori (abelian varieties). We make, via the Kowalewski-Painlevé analysis, a detailed study of the level manifolds of the system. These manifolds are described explicitly as being affine part of complex algebraic tori and the flow can be solved by quadrature, that is to say their solutions can be expressed in terms of abelian integrals. The Adler-van Moerbeke method’s which will be used is primarily analytical but heavily inspired by algebraic geometrical methods. We will also discuss several interesting examples of algebraic completely integrable systems.

The model of a rigid body and heavy foot joined by the revolute joint in the constant gravitational field is described. The rigid body moves in the vertical plane, whereas the heavy foot lies on the flat, very rough horizontal support. Conditions for the dynamic balance of this system are mathematically expressed by using the ZMP method. It is shown that they determine an area in the phase space in which the state of the system should be in order that its dynamic balance is kept. It is also shown by appropriate simulations of motion of the system in the dynamic balance that these conditions are not sufficient for the system to keep its upright posture, but are in connection with its controllability. It is briefly discussed what are the necessary conditions for this system in dynamic balance to keep its upright posture.

The deformation compatibility equation is built on the basis of the flexible treatment of the forcing pair,and the static binding force of forcing pairs of three pair bars space RCCR mechanism is solved under the condition of close to rigid body.The result is more concise and closing to the ideal state compared with that on the basis of the flexible treatment of the forcing bars.

A new concept of HILS(Hardware-In-the-Loop Simulation) system for an electric motor using the real-time coupling analysis with rigid body system and hydraulic system is presented in this paper. From the fuel consumption improvement point of view, the electric drive system is applied to the construction machinery for improving fuel efficiency and reducing pollution emissions. In the development of the electric drive system, it is important to evaluate the dynamic characteristics of the electric motor and control system, then HILS provides an approach for efficient development. This HILS system can act the actual load on the motor by calculating the coupling system equations of motion with the rigid body system and the hydraulic system in real-time. The real-time simulation was conducted by newly developed simulation model that the rigid bodies were actuated by the linear hydraulic actuator. A test rig was developed following this concept, in which the load computed by real-time simulation of the actual digging operation on the hydraulic excavator was exerted to the electric motor. The test results with developed testing system were compared with the simulation results using the simulation model with the electric motor. It is demonstrated that the HILS system of the electric motor can realize the actual digging operation of the hydraulic excavator.

Equations of plane-parallel sliding of a rigid body with the ring support under dry friction are derived. For the time of braking of a nonhomogeneous ring, we obtain a two-sided estimate which coincides with the "unimproved" estimate in the limit case of the narrow ring. As an example, the problem of braking of a system of two nearly situated narrow rings is considered.

This paper presents a real-time simulation for coupled system with rigid body system and hydraulic system. The equations of motion for the rigid body are derived by transforming the rigid body motion to the linear element motion. The system equations can be presented as the ordinary differential equations of motion for the coupled system of the rigid body system and the hydraulic system without introducing the constraint conditions, describing the motions of the rigid body system using the linear element motion. Then, this modeling is useful for the real time simulation for the coupled system, as numerical stability is improved by carrying out coupled system simulation in one software package. Firstly, rigid body system driven by the linear element is formulated, coupled analysis theory with the hydraulic system is derived, and electric motor drive system is formulated. Finally, the actual digging simulations of a hydraulic excavator are implemented using the present technique. It is clarified that the real time simulation is successfully conducted.

The paper investigates added mass quantity or, in other words, fluid inertia moment by which fluid resists to the change of its velocity. Fluid, as any other rigid substance, resists to the change of its velocity. In rigid substances the resistance equals the mass of rigid body while in fluids that mass cannot be known in advance, it has to be determined. Its determination is accompanied by certain difficulties due to fluid mass quantity, its physical and chemical properties as well as to the form and the law of rigid body velocity change while the body is moving through space filled with fluid.

The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis 3ˆ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT.

Equations of motion of an axially symmetric sphere rolling and sliding on a plane are usually taken as model of the tippe top. We study these equations in the nonsliding regime both in the vector notation and in the Euler angle variables when they admit three integrals of motion that are linear and quadratic in momenta. In the Euler angle variables (θ,φ,ψ) these integrals give separation equations that have the same structure as the equations of the Lagrange top. It makes it possible to describe the whole space of solutions by representing them in the space of parameters (D,λ,E) being constant values of the integrals of motion.

Apresentamos a forma geral do teorema dos eixos perpendiculares, a qual pode ser aplicada a qualquer corpo rígido, e obtemos a sua versão válida para qualquer sólido de revolução. Apresentamos, ainda, o seu caso particular para cilindros gerais retos. Alguns exemplos são feitos com o intuito de mostrarmos como pode ser simplificada a determinação de momentos de inércia de certos corpos rígidos se fizermos uso deste teorema.