Angular Degrees Of Freedom Research Articles

Modifications to ArduSub That Improve BlueROV SITL Accuracy and Design of Hybrid Autopilot

Improvements to ArduSub for the BlueROV2 (BROV2) Heavy, necessary for accurate simulation and autonomous controller design, were implemented and validated in this work. The simulation model was made more accurate with new data obtained from real-world testing and values from the literature. The manual control algorithm in the BROV2 firmware was replaced with one compatible with automatic control. In a Robot Operating System (ROS), a proportional–derivative (PD) controller to assist augmented reality (AR) pilots in controlling angular degrees of freedom (DOF) of the vehicle was implemented. Open-loop testing determined the yaw hydrodynamic model of the vehicle. A general mathematical method to determine PD gains as a function of the desired closed-loop performance was outlined. Testing was carried out in the updated simulation environment. Step response testing found that a modified derivative gain was necessary. Comparable real-world results were obtained using settings determined in the simulation environment. Frequency response testing of the modified yaw control law discovered that the bandwidth of the nonlinear system had a one-to-one correspondence with the desired closed-loop natural frequency of a simplified linear approximation. The control law was generalized for angular DOF and linear DOF were operated with open-loop control. A full six-DOF simulated dive demonstrated excellent tracking.

Design of a spherical parallel mechanism with controllable center of rotation using a spherical reconfiguration linkage

It is well known that Remote Center of the motion (RCM) mechanisms are highly suitable for many medical applications. While it is sometimes preferable that the mechanism can control their Center of Rotation (CoR), most RCM mechanisms do not have this possibility without being mounted on large and heavy translational platforms. By using a new concept of Spherical Reconfigurable Linkage (SRL), the present study offers an alternative solution. These new linkages are designed to control their radius and they are connected to form an RCM mechanism with controllable CoR. The newly mounted mechanism now has two linear Degrees of Freedom (DoF) for the displacement of its CoR in addition to its two angular DoF. The linear kinematic model is derived along with the angular kinematic one while taking into account the reconfiguration of the SRL. The velocity model is calculated and all singular configurations are identified. The mechanism performances in terms of workspace and kinematic performances are is also assessed. Finally, motion capture experiments on a prototype validated the models.

Consideration of the problem of motion cueing along angular degrees of freedom on flight simulators

The object of research is motion cueing along angular degrees of freedom on flight simulators of non-maneuvering aircraft. One of the most problematic places is lack of statement and effective solution of the problem to ensure high-quality motion cues along angular degrees of freedom on flight simulators, which would correspond to motion cues along angular degrees of freedom in real flight with the same control actions. In the course of the research, on the basis of the peculiarities of human movement perception, a set of characteristic attributes of perception of motion cues is determined: character, direction, duration, intensity and time of motion perception (according to Gibson’s perception theory). Based on the system approach principles, the mathematical formulation of the solution to the problem of motion cueing along angular degrees of freedom on flight simulators of non-maneuvering aircraft is used. Such approach made it possible, taking into account the existing constructive resource of flight simulator motion system, to bring as close as possible motion cueing along angular degrees of freedom on flight simulators of non-maneuvering aircraft to motion cues along angular degrees of freedom in real flight with the same control actions. Due to this the character and direction of motion cues fully correspond to the real motion cues, the difference between the perception time of motion cues on airplane and simulator is minimal and meets the current requirements. The duration and intensity of the motion cue perception on simulator are proportional duration and intensity of motion cue perception on airplane. Such approach significantly improves the quality of training and retraining of pilots on flight simulators. Implementation of the developed problem formulation on aircraft simulators, in particular on An-74TK-200, showed its high efficiency. In the future, the proposed approach can be used on flight simulators of aircraft developed in Ukraine and modernization of operated flight simulators.

H2O-HCN complex: A new potential energy surface and intermolecular rovibrational states from rigorous quantum calculations.

In this work the H2O-HCN complex is quantitatively characterized in two ways. First, we report a new rigid-monomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetry-adapted perturbation theory based on density functional theory method. The PES is based on 2833 abinitio points computed employing the aug-cc-pVQZ basis set, utilizing the autoPES code, which provides a site-site analytical fit with the long-range region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O-HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum bound-state methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged ground-state geometry of H2O-HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed ground-state rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O-HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.

Dipol'naya plazmonnaya moda v nanorazmernykh poluprovodnikovykh kvantovykh tochkakh tipa "yadro-obolochka" s geteroperekhodom vtorogo roda

Excited states of nanosize two-component semiconductor core–shell crystals with a type II heterojunction are analyzed. It is demonstrated that the dipole plasmon resonance dominates in their photoabsorption spectra. It is found that the variation of the potential barrier height between the core and the shell in a comparatively narrow range leads to a fundamental change in the form of the collective mode from the surface plasmon resonance typical of the photoabsorption spectra of conducting nanosize particles to the rotational plasmon mode, for which only angular degrees of freedom are excited.

Fast, low-memory numerical methods for radiative transfer via hp-adaptive mesh refinement

Numerical solutions to the radiative transfer equation are typically computationally expensive. The large expense arises because the solution has a high dimensionality with NM degrees of freedom, where the N and M arise from spatial and angular degrees of freedom, respectively. Here, a numerical method is presented that aims for fast and low-memory calculations, in the sense of computational cost and memory requirements of only O(N). The method uses a discontinuous Galerkin (DG) spectral element method and hp-adaptive mesh refinement to reduce the number of spatial degrees of freedom from N to n, thereby reducing the total cost and memory to nM, with the aim of achieving nM approximately equal to N. After this reduction in memory to O(N), in order to ensure a computational cost of O(N), a suitable preconditioner is identified and utilized. Numerical examples are presented in two spatial dimensions to allow calculation of high-resolution reference solutions for comparison, while the methodology is general and applies in either two or three spatial dimensions. The numerical examples show large memory reduction ratios N/n and fast O(N) computational cost. A variety of examples is shown, including smooth spatial variations or steep gradients, and Rayleigh (isotropic) or Mie (anisotropic) scattering. The methods could enable more tractable computations for many applications, such as medical imaging and weather and climate prediction.

New Class of Polymer Materials-Quasi-Nematic Colloidal Particle Self-Assemblies: The Case of Assemblies of Prolate Spheroidal Poly(Styrene/Polyglycidol) Particles.

Assemblies of colloidal polymer particles find various applications in many advanced technologies. However, for every type of application, assemblies with properly tailored properties are needed. Until now, attention has been concentrated on the assemblies composed of spherical particles arranged into so-called perfect colloidal crystals and on complex materials containing mixtures of crystal and disordered phases. However, new opportunities are opened by using assemblies of spheroidal particles. In such assemblies, the particles, in addition to the three positional have three angular degrees of freedom. Here, the preparation of 3D assemblies of reference microspheres and prolate spheroidal poly(styrene/polyglycidol) microparticles by deposition from water and water/ethanol media on silicon substrates is reported. The particles have the same polystyrene/polyglycidol composition and the same volumes but differ with respect to their aspect ratio (AR) ranged from 1 to 8.5. SEM microphotographs reveal that particles in the assembly top layers are arranged into the quasi-nematic structures and that the quality of their orientation in the same direction increase with increasing AR. Nano- and microindentation studies demonstrate that interactions of sharp and flat tips with arrays of spheroidal particles lead to different types of particle deformations.

Rigid diatomic polar molecules in an external uniform electric field

This paper presents a didactic treatment of the rigid diatomic molecule under the action of an external electric field. We discuss the role of a new constant of motion that is valid when the electric field breaks spherical symmetry. We obtain the wave functions and the energies in the radial direction as well as the angular degrees of freedom, the latter corresponding to the eigenvalue spectrum of the new constant of motion. We apply the theory of the HBr molecule, and plot some of its eigenfunctions to show how they deform under the presence of an electric field. We calculate the wave lengths of the absorbed electromagnetic radiation in the transition of the first and second excited states and with different field values.

Overconstrained models of time delay lenses redux: how the angular tail wags the radial dog

Abstract The two properties of the radial mass distribution of a gravitational lens that are well constrained by Einstein rings are the Einstein radius RE and ξ2 = REα″(RE)/(1 − κE), where α″(RE) and κE are the second derivative of the deflection profile and the convergence at RE, respectively. However, if there is a tight mathematical relationship between the radial mass profile and the angular structure, as is true of ellipsoids, an Einstein ring can appear to strongly distinguish radial mass distributions with the same ξ2. This problem is beautifully illustrated by the ellipsoidal models in Millon et al. When using Einstein rings to constrain the radial mass distribution, the angular structure of the models must contain all the degrees of freedom expected in nature (e.g. external shear, different ellipticities for the stars and the dark matter, modest deviations from elliptical structure, modest twists of the axes, modest ellipticity gradients, etc.) that work to decouple the radial and angular structures of the gravity. Models of Einstein rings with too few angular degrees of freedom will lead to strongly biased likelihood distinctions between radial mass distributions and very precise but inaccurate estimates of H0 based on gravitational lens time delays.

New Way To Determine The Technical Condition Of Ball Joints

Among the multitude of vehicle suspension assemblies, the ball joint is one of the most important bearing assemblies, the operability of which directly depends on the operating conditions. Ball joints are used to connect the suspension and steering components and are kinematic interfaces that have three angular degrees of freedom when moving the working elements (levers). The reliability of the hinges has a significant impact on the safety of the car. In most cases, the ball joint is an indiscriminate node, which makes it difficult to determine the technical condition in a car service center. One of the methods of diagnosing are laboratory bench examinations of ball joints. To obtain reliable information about the wear of ball joints and the development of a technique for determining their technical condition in the conditions of an auto service company, a laboratory bench research area is needed. The completed research aimed at developing methods, tools and algorithms for determining the technical state of ball joints in the conditions of an auto service company. As a result of the research, the author’s team developed a vibration method for determining the technical state of ball joints and a mathematical model for changing the technical condition of the ball joint of the front suspension of the MacPherson type of a car, in bench tests.

Spherical pendulum model with a moving suspension point in the problem of spatial load movement by a hoisting crane with oscillation limiting

The task of controlling the load spatial oscillations of a hoisting crane using a spherical pendulum model with two angular degrees of freedom is considered. In order to limit uncontrolled load oscillations, its suspension point movements are optimised. The system of differential nonlinear equations for oscillations of a spherical pendulum with suspension point acceleration along the Cartesian axes was first applied to the curvilinear load moving in the limiting oscillations. Sigmoidal dependences of two load deviation angles and rotation of the pendulum are proposed, providing for expressions of the first two derivatives of the indicated angles, as well as linear accelerations of the load suspension point along two Cartesian horizontal axes. Numerical methods are applied to obtain time dependences of the velocities and displacements of the load suspension point. The solution provides the load moving along a curvilinear trajectory at specified distances along the specified axes, subject to the maximum acceleration and crane speed limitations. Optimal time dependences of the rope deflection angles, suspension point displacements and their first two derivatives in limited oscillations are presented. The scope of the methodology is the modelling of crane working processes and the automatic movement control for the bridge and gantry cranes.

Angular and spatial light modulation by single digital micromirror device for multi-image output and nearly-doubled étendue

The "Angular Spatial Light Modulator" (ASLM) achieves simultaneous angular and spatial light modulation at a plane by combining Digital Micromirror Device (DMD) based programmable blazed grating beam steering and binary pattern sequencing. The ASLM system multiplies the number of effective output pixels of the DMD for increased spatial and/or angular degrees of freedom, and nearly-doubles the étendue output of the DMD. We implement multiple illumination and projection schemes to demonstrate ASLM-based extended FOV display, light-field projection, and multi-view display. We also implement time-multiplexed pupil segmented illumination to extend the pattern steering to two dimensions.

Description of critical point nuclei within an energy-dependent geometric model

An exactly solvable version of the Bohr Hamiltonian is proposed for a unified treatment of transitional nuclei. The model employs an energy-dependent potential in the \( \beta\) shape variable which is amended with a centrifugal contribution from the \( \gamma\) and angular degrees of freedom. The parametrization of the \( \gamma\) part of the potential enables the connection between the adiabatic separation of \( \beta\) and \( \gamma\) fluctuations suitable for critical point nuclei and the exactly separable solutions specific to deformed nuclei. The fully analytical model is applied to known critical point nuclei as well as a neighbouring isotope for each case. Beside very good agreement with experiment for energies and electromagnetic transitions, numerical results also reveal specific model characteristics for critical nuclei in comparison to more or less deformed nuclei.

An angular multigrid preconditioner for the radiation transport equation with Fokker–Planck scattering

In a previous paper (Hennink and Lathouwers, 2017) we developed a finite element discretization for the Boltzmann transport equation with forward peaked scatter modeled by the Fokker–Planck approximation. The discretization was based on the discontinuous Galerkin method in both space and angle. It was expected and found that the regular source iteration algorithm for the Boltzmann equation is not effective in solving the discretized system and becomes excessively expensive for problems with many angular degrees of freedom. The purpose of this paper is to develop a multigrid scheme as preconditioner for the above mentioned discretization. The method exploits the nested nature of the meshes and the natural prolongation/restriction between meshes by Galerkin projection. A set of test problems ranging from pure spherical diffusion to the complete Boltzmann transport problem in 3D are presented to illustrate that the method is very effective, resulting in iteration counts nearly independent of problem size even for highly non-isotropically refined angular meshes.

Radial-angular entanglement in Laguerre-Gaussian mode superpositions.

Classical optic entanglement between the radial and angular degrees of freedom in Laguerre-Gaussian mode superpositions is explored within the framework of symmetric first-order optical systems. The Gouy phase picked by a Laguerre-Gaussian mode on free propagation is seen to be of consequence to the radial-angular entanglement in the mode superpositions. We illustrate examples of mode superpositions for which radial-angular entanglement is preserved on passage through symmetric first-order optical systems. An indicator of radial-angular entanglement in two-mode Laguerre-Gaussian superpositions is demonstrated to be a robust free space signaler in the presence of atmospheric turbulence, through examples.

Geometrical product specifications. Datums and coordinate systems

The work is devoted to the relevant topic such as the technical products quality improvement due to the geometrical specifications accuracy. The research purpose is to ensure the quality indicators on the basis of the systematic approach to the values normalization and geometrical specifications accuracy in the workpiece coordinate systems in the process of design. To achieve the goal two tasks are completed such as the datum features classification according to the number of linear and angular freedom degrees constraints, called the datums informativeness, and the rectangular coordinate systems identification, materialized by workpiece datums sets. The datum features informativeness characterizes the datums functional purpose to limit product workpiece linear and angular degrees of freedom. The datum features informativeness numerically coincides with the kinematic pairs classes and couplings in mechanics. The datum features informativeness identifies the coordinate system without the location redundancy. Each coordinate plane of a rectangular coordinate system has different informativeness 3 + 2 + 1. Each coordinate axis also has different informativeness 4+2+Θ (zero). It is possible to establish the associated workpiece position with three linear and three angular coordinates relative to two axes with the informativeness 4 and 2. is higher, the more informativeness of the coordinate axis or a coordinate plane is, the higher is the linear and angular coordinates accuracy, the coordinate being plotted along the coordinate axis or plane. The systematic approach to the geometrical products specifications positioning in coordinate systems is the scientific basis for a natural transition to the functional dimensions of features position - coordinating dimensions and the size of the features form - feature dimensions of two measures: linear and angular ones. The products technical quality improving is possible due to the coordinate systems introduction materialized by datums sets in GPS standards and national standards. Standards on the datums and datums systems should cover all the geometrical specifications and all the processes of the products life cycle: designing, manufacturing, verification and exploitation.

Laser-Controlled Torsions: Four-Dimensional Theory and the Validity of Reduced Dimensionality Models.

A multitude of possible applications along with unique coherence, chirality, and symmetry properties makes the control of molecular torsion with moderately strong, nonresonant laser pulses a fascinating subject. A description of combined rotation and torsion requires at least four angular degrees of freedom, which is challenging for the majority of systems. Lower-dimensional models have been proposed but also questioned. Here, we develop a four-dimensional model for the coupled rotational-torsional motions of molecules consisting of two identical moieties. By comparing four-dimensional calculations with a two-dimensional model, we define conditions under which the lower-dimensional model is valid. In particular, we point to the crucial role of coordinate dependence of the polarizability tensor. Our results do not agree with those of previous four-dimensional calculations but support the conclusions of recent experiments.

J-factors of short DNA molecules.

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain end boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length (N) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

Geometrical product specifications: A structure of linear dimensions tolerances

The paper reveals the relationship of linear dimensions tolerances with other geometrical specifications: coordinates, deviations of position and deviations of surface configuration of component geometric features. The dependence of the precision structure of the linear dimensions on the functional purpose of features. The basic concept of the paper is informativeness of the feature, which represents the total number of linear and angular degrees of freedom, constrained by the feature in the component at operation. The very informativeness of the feature determines the two-dimensional linear-angular composition of the structure of the linear size, its tolerance and standard grade. This paper discusses only the linear dimensions of the features involved in couplings and forming fits.