Rotational Motion Of Rigid Body Research Articles

Nonlinear dynamic characteristics of horizontal-axis wind turbine blades including pre-twist

This paper focuses on the dynamic modeling and vibration analysis of horizontal axis wind turbine (HAWT) blades with emphasis on the effects of the pre-twist, rotational rigid body motion and coupling among the different blade's degrees of freedom. The blade is considered as a rotating pre-twisted beam mounted on a rigid hub with a constant angle relative to the plane of rotation, so-called precone angle. Kinetic energy of the blade based on its elastic as well as rigid motion together with its strain energy and generalized forces resulting from gravitational, centrifugal and aerodynamic loadings are obtained and used to derive new coupled dynamic equations by means of Hamilton's principle. The weak formulation is constructed and the Rayleigh-Ritz method (RRM) is adopted to extract a reduced order model (ROM) for the blade's vibration analysis. The developed nonlinear ROM is linearized around the steady-state solution and the blade's dynamic characteristics are obtained. The reference wind turbine blade called NREL 5-MW HAWT blade is selected as the case-study and effects of pre-twist, centrifugal force, angular velocity-depended terms, nonlinearities and transverse static loads on its dynamic characteristics are investigated. Results are shown to be in good agreement with available data in the literature.

Forming Computational Thinking and Computer Modeling Project Activities in the Physics Course of the Technical University

The article discusses contextual technology of teaching and learning physics of IT students at the Technical University. The main goal of this research is development and analysis contextual technology to maintain and increase IT students’ interest in physics with parallel formation of computational thinking and competencies in computer science applications. This technology takes place in several contexts: the scientific method and modeling of physical processes, computational thinking and professional competence. The all contexts are present in four stages of the training cycle: lectures, seminars, lab works, and computer modeling of physical processes. As an example we demonstrate using the contextual technology for the physics course topic “Dynamics of a rigid body rotational motion” in all four stages of the training cycle. The example of student’s team development of the virtual lab work “Precession and nutation of a gyroscope” is given. According to the Novosibirsk State Technical University professors and students, the author’s technology has demonstrated its effectiveness in the formation of professional thinking and competencies of the IT students in teaching physics at the Technical University.

System identification and robust attitude control of an unmanned helicopter using novel low-cost flight control system

In recent years, unmanned aerial systems have attracted great attention due to the electronic systems technology advancements. Among these vehicles, unmanned helicopters are more important because of their special abilities and superior performance. The complex nonlinear dynamic system (caused by main rotor flapping dynamics coupled with the rigid body rotational motion) and considerable effects of ambient disturbance make their utilization hard in actual missions. Attitude dynamics have the main role in helicopter stabilization, so implementing proper control system for attitude is an important issue for unmanned helicopter hovering and trajectory tracking performance. Besides this, experimental utilization of low-cost flight control system for unmanned helicopters is still a challenging task. In this article, dynamic modeling, system identification, and robust control system implementation of roll and pitch dynamics of an unmanned helicopter is performed. A TRex-600E radio-controlled helicopter is equipped with a novel low-cost flight control system designed and constructed based on Raspberry Pi Linux-based microcomputer. Using Raspberry Pi makes this platform simpler to utilize and more time and cost-effective than similar platforms used before. The experiments are performed on a 5-degree-of-freedom testbed. The robust control system is designed based on [Formula: see text] method and is evaluated in real flight tests. The experiment results show that the proposed platform has the ability to successfully control the roll and pitch dynamics of the unmanned helicopter.

Ellipsoidal state estimation based on sum of squares for non‐linear systems with unknown but bounded noise

This brief concerns the set-theoretic recursive state estimation of non-linear systems with polynomial dynamics, making use of ellipsoidal bounds. The sum of squares approach is used to construct an optimal ellipsoid containing the intersection of sets obtained with the use of non-linear system equations and measurement equations. The properties of the proposed filter are illustrated with two examples, one concerning the simultaneous estimation of parameters and state of a linear system, and the other on the Euler equations of the rigid body rotational motion.

Vision-Based Relative Navigation Using Dual Quaternion for Spacecraft Proximity Operations

Dual quaternion is the parameter that can describe position and attitude in a unified form. It is extension of dual number and quaternion; so, mathematical and parameter characteristics of those are holding. The attitude and orbital kinematics model can be concurrently integrated in a simplified and intuitive formulation with dual quaternion. From these merits, dual quaternion-based relative navigation for spacecraft proximity operation is investigated in this paper. Especially, the case is considered which interested points are not coincident with center of mass of spacecraft. At this time, it is obvious that position is affected by rotational motion of rigid body. With conventional decoupled relative kinematics, this attitude–position coupling effect cannot be described at once. However, the new dual quaternion-based relative kinematics can represent coupled orbital motion in a simple form. Motivated by these backgrounds, in this paper, to estimate relative position and attitude states using vision sensor, dual quaternion-based relative kinematics is formulated. To reduce the number of state variables, error dual quaternion is applied, which makes the number of state variable be six instead of eight, by using parameter constraints of dual quaternion. Extended Kalman filter and unscented Kalman filter are adopted to realize relative navigation. Since the necessity of velocity information in dual quaternion kinematics, two types system models are constructed—velocity propagation and velocity measurement model. In addition, the six line-of-sight measurements are used to update the dual quaternion parameter. Simulation results show that the kinematics model is accurately derived, states are well estimated, and statistics of estimation errors are consistent with estimated error covariance.

On the existence of new integrable cases for Euler-Poisson equations in Newtonian fields

In this article, the rotational motion of a non-symmetric rigid body about a fixed point under the action of multi-Newtonian centers located on one fixed axis is considered. The aim of the work is to derive a technique to obtain such new (particular) integrable cases for the rotational motion of a rigid body in newtonian field of forces whose centers located on the vertical fixed axis. This technique reduces the governing equations and their known first integrals describing the motion to the unknown fourth integral and new system of differential equations. The well-known fourth integral cases are tested to verify the validity of the derived system and some new (particular) integrable cases are obtained with their geometrical interpretations of motion. The particular scope from this work is to extend Arkangel’skii’s theorem and the other related theorems to obtain such new integrable cases of single valuedness of solutions for this problem and its related special cases.

Spacecraft Attitude Fractional Feedback Control Using Rotation Matrices and Exponential Coordinates

Two fractional proportional–integral–derivative controllers are proposed for rigid spacecraft rotational dynamics. In the first strategy, the controller is developed on the tangent bundle of SO(3), which is the Lie group of rigid-body rotational motion, using states consisting of a rotation matrix and an angular velocity vector in the fractional-order derivative and integral feedback terms. In the second strategy, the exponential coordinates are used to design the controller. The fractional derivative and integral feedback terms have adjustable orders that can be used to tune the closed-loop response. The performances of the controllers are studied numerically for different values of the derivative and integral fractional orders in terms of control effort, steady-state response characteristics, and robustness to unmodeled disturbances; and the results are compared with those of an integer-order controller. It is shown that the inclusion of fractional orders in the controllers allows for a desired shape and spectrum of the controlled response to be obtained by tuning the fractional derivative and integral orders. For instance, the settling time and control effort may be simultaneously reduced, in contrast to the case of integer feedback control in which a tradeoff exists between these competing design specifications. The proposed fractional feedback attitude control strategies thus allow for a greater degree of flexibility over their integer-order analogs.

Smartphone based scalable reverse engineering by digital image correlation

There is a need for scalable open source 3D reconstruction systems for reverse engineering. This is because most commercially available reconstruction systems are capital and resource intensive. To address this, a novel reconstruction technique is proposed. The technique involves digital image correlation based characterization of surface speeds followed by normalization with respect to angular speed during rigid body rotational motion of the specimen. Proof of concept of the same is demonstrated and validated using simulation and empirical characterization. Towards this, smart-phone imaging and inexpensive off the shelf components along with those fabricated additively using poly-lactic acid polymer with a standard 3D printer are used. Some sources of error in this reconstruction methodology are discussed. It is seen that high curvatures on the surface suppress accuracy of reconstruction. Reasons behind this are delineated in the nature of the correlation function. Theoretically achievable resolution during smart-phone based 3D reconstruction by digital image correlation is derived.

Theory of Kinematic Motion Control of a Rigid Body

The authors present a review of the works on the theory of kinematic control of the rotational (angular) motion of a rigid body and spatial motion of a free rigid body, which is a composition of the rotational and translational (trajectory) movements of a rigid body. The theory is based on the use of the quaternion and biquaternion kinematic models of the rigid body motion. They also provide a review of the papers devoted to the problems of construction of the optimal laws of change of the angular momentum of a dynamically symmetric rigid body and rigid body with an arbitrary mass distribution, which ensures its optimal translation from an arbitrary initial angular position to the desired final angular position. These tasks occupy an intermediate position between the kinematic and dynamic problems of control of the rotational rigid body motion and play an important role in the theory of control of orientation of the spacecraft using the rotating flywheels. The theory of kinematic motion control has various topical applications in the space flight mechanics, inertial navigation, and mechanics of robotics.

Analyzing Free-Free Beams by Green's Functions and Fredholm Alternative Theorem

AbstractThis article deals with the analysis of free-free beams by an analytical method. The well-known Green's function method is employed, and exact solution for the problem is obtained. As a second problem, the simply supported-free beam with rotational rigid body motion is analyzed. It is initially shown that ordinary Green's functions cannot be constructed due to a mathematical contradiction. To remedy this limitation, the Fredholm Alternative Theorem is utilized. This theorem eliminates the contradiction and enables analysts to obtain modified Green's functions. The fundamental existence conditions are derived and thoroughly investigated from the structural point of view. Finally, the deflection functions of these beams are found using modified Green's functions.

Synthesis of Time Optimal Spatial Slewing of Spacecraft Using Dynamic Equation of Rigid Body Rotational Motion at Rodrigues-Hamilton Parameters

Synthesis of Time Optimal Spatial Slewing of Spacecraft Using Dynamic Equation of Rigid Body Rotational Motion at Rodrigues-Hamilton Parameters

Analytical evaluation of dynamic characteristics of unanchored circular ground-based steel tanks

Natural and rocking frequencies of liquid-filled unanchored cylindrical steel tanks are determined using an analytical approach. In the proposed simplified mechanical model, the bottom plate of the tank is replaced by equivalent rotational and vertical springs. To evaluate natural frequencies, potential and kinetic energies of the liquid-filled tank are utilized and the eigen equation is solved by applying the Lagrange method and Ritz-type mode shapes for elastically supported cylindrical shells. Formulas are also derived to determine the rocking frequency based on a rotational rigid body motion and results are verified with available experimental data. Also, effect of the increase in kinetic energy of the tank during rocking motion on the natural frequencies of the tank is explored. To investigate the effects of tank geometrical aspect ratios on the structural responses, three models with height to diameter ratios of 0.4 (squat tank), 0.63 (medium tank) and 0.9 (slender tank) are considered. The results obtained using the proposed simplified mechanical model indicate that the method is capable of determining the rocking frequency of unanchored steel liquid-filled tanks with acceptable accuracy. Also, it is shown that at the onset of rocking mode, the fundamental natural frequency of the tank decreases considerably.

FLEXIBLE DYNAMIC MODEL OF ATTITUDE MANEUVERING OF RAZAKSAT® SATELLITE

In this paper, a dynamic model equation of the RazakSAT® class satellite three flexible solar panels for three-dimensional dynamic studies is developed based on the coupling deformation field. In the model, each solar panel is flexible and attached to the satellite body via a fixed joint where the assumption of Euler-Bernoulli beam is applied for the solar panels. Lagrange and assumed mode method are used to develop the dynamic model of the RazakSAT® multi-body system. A comprehensive model of flexible satellite has been provided in ANSYS environment as a reference when simulating the theoretical response generated by MATLAB to show that the coupling effect on the characteristics of the flexible sub system while undergoing rigid-body rotational motion.

Crystal structure of the Mycobacterium tuberculosis transcriptional regulator Rv0302.

Mycobacterium tuberculosis is a pathogenic bacterial species, which is neither Gram positive nor Gram negative. It has a unique cell wall, making it difficult to kill and conferring resistance to antibiotics that disrupt cell wall biosynthesis. Thus, the mycobacterial cell wall is critical to the virulence of these pathogens. Recent work shows that the mycobacterial membrane protein large (MmpL) family of transporters contributes to cell wall biosynthesis by exporting fatty acids and lipidic elements of the cell wall. The expression of the Mycobacterium tuberculosis MmpL proteins is controlled by a complicated regulatory network system. Here we report crystallographic structures of two forms of the TetR-family transcriptional regulator Rv0302, which participates in regulating the expression of MmpL proteins. The structures reveal a dimeric, two-domain molecule with architecture consistent with the TetR family of regulators. Comparison of the two Rv0302 crystal structures suggests that the conformational changes leading to derepression may be due to a rigid body rotational motion within the dimer interface of the regulator. Using fluorescence polarization and electrophoretic mobility shift assays, we demonstrate the recognition of promoter and intragenic regions of multiple mmpL genes by this protein. In addition, our isothermal titration calorimetry and electrophoretic mobility shift experiments indicate that fatty acids may be the natural ligand of this regulator. Taken together, these experiments provide new perspectives on the regulation of the MmpL family of transporters.

Crystal Structure of the Transcriptional Regulator Rv0678 of Mycobacterium tuberculosis

Recent work demonstrates that the MmpL (mycobacterial membrane protein large) transporters are dedicated to the export of mycobacterial lipids for cell wall biosynthesis. An MmpL transporter frequently works with an accessory protein, belonging to the MmpS (mycobacterial membrane protein small) family, to transport these key virulence factors. One such efflux system in Mycobacterium tuberculosis is the MmpS5-MmpL5 transporter. The expression of MmpS5-MmpL5 is controlled by the MarR-like transcriptional regulator Rv0678, whose open reading frame is located downstream of the mmpS5-mmpL5 operon. To elucidate the structural basis of Rv0678 regulation, we have determined the crystal structure of this regulator, to 1.64 Å resolution, revealing a dimeric two-domain molecule with an architecture similar to members of the MarR family of transcriptional regulators. Rv0678 is distinct from other MarR regulators in that its DNA-binding and dimerization domains are clustered together. These two domains seemingly cooperate to bind an inducing ligand that we identified as 2-stearoylglycerol, which is a fatty acid glycerol ester. The structure also suggests that the conformational change leading to substrate-mediated derepression is primarily caused by a rigid body rotational motion of the entire DNA-binding domain of the regulator toward the dimerization domain. This movement results in a conformational state that is incompatible with DNA binding. We demonstrate using electrophoretic mobility shift assays that Rv0678 binds to the mmpS5-mmpL5, mmpS4-mmpL4, and the mmpS2-mmpL2 promoters. Binding by Rv0678 was reversed upon the addition of the ligand. These findings provide new insight into the mechanisms of gene regulation in the MarR family of regulators.

Structural and functional analysis of the transcriptional regulator Rv3066 of Mycobacterium tuberculosis

The Mmr multidrug efflux pump recognizes and actively extrudes a broad range of antimicrobial agents, and promotes the intrinsic resistance to these antimicrobials in Mycobacterium tuberculosis. The expression of Mmr is controlled by the TetR-like transcriptional regulator Rv3066, whose open reading frame is located downstream of the mmr operon. To understand the structural basis of Rv3066 regulation, we have determined the crystal structures of Rv3066, both in the absence and presence of bound ethidium, revealing an asymmetric homodimeric two-domain molecule with an entirely helical architecture. The structures underscore the flexibility and plasticity of the regulator essential for multidrug recognition. Comparison of the apo-Rv3066 and Rv3066–ethidium crystal structures suggests that the conformational changes leading to drug-mediated derepression is primarily due to a rigid body rotational motion within the dimer interface of the regulator. The Rv3066 regulator creates a multidrug-binding pocket, which contains five aromatic residues. The bound ethidium is found buried within the multidrug-binding site, where extensive aromatic stacking interactions seemingly govern the binding. In vitro studies reveal that the dimeric Rv3066 regulator binds to a 14-bp palindromic inverted repeat sequence in the nanomolar range. These findings provide new insight into the mechanisms of ligand binding and Rv3066 regulation.

Calculation of the electric field resulting from human body rotation in a magnetic field

A number of recent studies have shown that the electric field and current density induced in the human body by movement in and around magnetic resonance imaging installations can exceed regulatory levels. Although it is possible to measure the induced electric fields at the surface of the body, it is usually more convenient to use numerical models to predict likely exposure under well-defined movement conditions. Whilst the accuracy of these models is not in doubt, this paper shows that modelling of particular rotational movements should be treated with care. In particular, we show that v × B rather than −(v · ∇)A should be used as the driving term in potential-based modelling of induced fields. Although for translational motion the two driving terms are equivalent, specific examples of rotational rigid-body motion are given where incorrect results are obtained when −(v · ∇)A is employed. In addition, we show that it is important to take into account the space charge which can be generated by rotations and we also consider particular cases where neglecting the space charge generates erroneous results. Along with analytic calculations based on simple models, boundary-element-based numerical calculations are used to illustrate these findings.

Quasi-static consideration of high-frequency modes for more efficient flexible multibody simulations

A number of sets of modes, for example eigenmodes, constraint modes, inertia-relief attachment modes, may be used to describe the linear elastic deformation of a flexible body in multibody dynamics. It is always possible to transform modes so that the conditions of the Buckens-frame are fulfilled. The latter frame leads to serious simplifications in the equations of motion, but cannot avoid a coupling between the body’s rotational rigid body motion and its elastic deformation. In the present paper the deformation modes will be subdivided into low- and high-frequency modes. It will be shown that the latter-mentioned coupling effect of the second ones can be safely neglected in comparison with the first ones. Consequently, the high-frequency components can be removed from time integration at all, which leads to significant savings of computational effort while the accuracy regarding the body’s deformation remains almost the same. In the case of a known frequency content of external excitation, an algorithm is given so that the available modes can be automatically separated into such low- and high-frequency modes. While the number of low-frequency modes remains more or less constant, there is a significant trend to use an increased number of high-frequency modes. Examples are moving loads (e.g., guidance) or distributed loads as they occur in contact problems or when fluid pressure is acting on surfaces. A final numerical example is given in order to demonstrate the potential of the proposed method.

Integration of rotational algorithms into dissipative particle dynamics: modeling polyaromatic hydrocarbons on the meso-scale

Heavy crude oil consists of thousands of compounds, a significant fraction of which have fairly large molecular weights and complex structures. Our work aims at constructing a meso-scale platform to explore this complex fluid in terms of microstructure, phase behavior, stability and rheology. In the present study, we focus on the treatment of the structures of fused aromatic rings as rigid body fragments in fractions such as asphaltenes and resins. To derive the rotational motion of rigid bodies in a non-conservative force field, we conduct a comparison of three rigid body rotational algorithms integrated into a standard dissipative particle dynamics (DPD) simulation. The simulation results confirm the superiority of the Quaternion method. To ease any doubt concerning the introduction of rigid bodies into DPD, the performance of the Quaternion method was tested carefully. Finally, the aggregation dynamics of asphaltene in very diluted toluene was investigated. The nanoaggregates are found to experience forming, breaking up and reforming. The sizes of the asphaltene monomer and nanoaggregate are identified. The diffusion coefficient of diluted asphaltene in toluene is similar to that found experimentally. All these results verify the rotational algorithm and encourage us to extend this platform to study the rheological and colloidal characteristics of heavy crude oils in the future.

Rigid-Body Attitude Control

Rigid-body attitude control is motivated by aerospace applications that involve attitude maneuvers or attitude stabilization. The set of attitudes of a rigid body is the set of 3 X 3 orthogonal matrices whose determinant is one. This set is the configuration space of rigid-body attitude motion; however, this configuration space is not Euclidean. Since the set of attitudes is not a Euclidean space, attitude control is typically studied using various attitude parameterizations. Motivated by the desire to represent attitude both globally and uniquely in the analysis of rigid-body rotational motion, this article uses orthogonal matrices exclusively to represent attitude and to develop results on rigid-body attitude control. An advantage of using orthogonal matrices is that these control results, which include open-loop attitude control maneuvers and stabilization using continuous feedback control, do not require reinterpretation on the set of attitudes viewed as orthogonal matrices. The main objec tive of this article is to demonstrate how to characterize properties of attitude control systems for arbitrary attitude maneuvers without using attitude parameterizations.