Radius Vector Research Articles

On periodic modes of motion of a vibrating robot in a horizontal plane with anisotropic friction

The study of various celestial bodies is of great interest at the present time. Soil studies are being conducted. Vibrating robots could be possible tools for implementing the missions involving moving on the surface of celestial bodies. At the same time, such missions must be safe and sustainable. Such missions are very expensive. And they require high-quality modeling. The dynamics of a vibrating robot is investigated in this work. These structures can move on the surface of various celestial bodies, such as Mars, the Moon or asteroids. Various models can be used as a model of the contact interaction of bodies with a surface, in particular the Amonton-Coulomb law of friction.This paper is aimed at studying a mechanical system consisting of a rigid body (outer body) placed on a horizontal rough plane and of an internal moving mass moving inside the outer body in a circle lying in a vertical plane, so that the radius vector of the point has a constant angular velocity. Based on the general properties of the solutions, possible periodic modes and their features depending on the parameters of the problem are considered. All qualitatively different solutions in this case are described.

An Autotuning Hybrid Method with Bayesian Optimization for Road Edge Extraction in Highway Systems from Point Clouds

In transportation infrastructure systems, feature images and spatial characteristics are generally utilized as complementary elements derived from point clouds for road edge extraction, but the involvement of one or more hyperparameters in each makes the extraction complicated. This study proposes an autotuning hybrid method with Bayesian optimization for road edge extraction in highway systems. The hybrid method combines the strengths of 2D feature images and 3D spatial characteristics while also automatically tuning the hyperparameter combination using Bayesian optimization. The hyperparameters encompass high and low pixel gradient thresholds, neighborhood radius, and normal vector threshold. Later, the point cloud dataset of national highways in Henan Province, China, is taken as the case study to evaluate the performance of the proposed method against three benchmark methods in two typical road scenarios: straight and curved edges. Experimental results show that the proposed method outperforms the benchmarks in detection quality and accuracy. It can serve as a decision-making tool to complement traditional manual road surveying, enabling efficient and automated road edge extraction in highway systems.

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

Displacement norm in the presence of an inverse-square perturbing acceleration in the reference frame associated with the radius vector

The problem of motion of a zero-mass point under the influence of attraction to the central body and a small perturbing acceleration P′ = P/r 2 is considered, where r is the distance to the attracting center, components of the vector P are assumed to be constant in a reference system with axes directed along the radius vector, the transversal and the angular momentum vector. Previously, for this problem, we found equations of motion in the mean elements and formulas for the transition from the osculating elements to the mean elements in the first order of smallness; we neglected second-order quantities. In this work, the Euclidean (root–mean–square over the mean anomaly) displacement norm ||dr||2 is obtained, where dr represents the difference between the position vectors on the osculating and mean orbit. It turned out that ||dr||2 depends only on the components of the vector P (positive definite quadratic form), the semi–major axis (proportional to the second power) and the eccentricity of the osculating ellipse. The norm ||dr||2 is obtained in the form of series in powers of the β=e/1+1-e2and in powers of the eccentricity e. The results are applied to the problem of the motion of asteroids under the influence of a perturbing acceleration inversely proportional to the square of the heliocentric distance, in particular, under the influence of the Yarkovsky effect.

OPTIMIZATION OF GEOMETRY OF PIEZORESISTIVE EFFECT ON THE EXAMPLE OF CUBIC CRYSTALS

On the example of semiconductor crystals Ge, Si, PbTe, PbS, InSb with different levels of doping and different types of conductivity, the geometry of the piezoresistive effect was optimized, namely, such directions of voltage measuring and uniaxial pressure applying were determined, which ensure the maximum achievable value of the effect. The optimization is based on an approach using the construction and analysis of extreme surfaces that represent all possible maxima of the objective function (the magnitude of the effect) under different spatial orientations of interacting factors. The optimization parameters were the angles that determine the directions of the unit vectors of the directions of current and uniaxial pressure applying. The directions of the radius vectors of the points on the extreme surface coincide with the ones in which the electric voltage is measured, and the length of this radius vector for each point was determined by setting such optimization parameters for which the magnitude of the effect for a given direction of voltage measuring would be maximal. It is shown that the optimal interaction geometry in most of the studied cases is longitudinal, and only for n-PbTe, p-InSb crystals it is transverse (although not identical), and the optimal directions for the studied crystals are <100>, <110> or <111> depending on the composition of the crystal and the type of doping. Despite the fact that all investigated crystals belong to the same point symmetry group (m3m), the shapes of the extreme surfaces for them are significantly different, which is caused by different ratios between the piezoresistive coefficients. Typical forms of extreme surfaces have been identified, and in order to explain the obtained results, an analysis of limiting cases that differ in the ratio of piezoresistive coefficients has been carried out. Based on this analysis, four main types of extreme surfaces were established. A scheme has been built that allows, in the case of cubic crystals, to estimate the type of extreme surface and the corresponding optimal directions of voltage measuring, current density (for cubic crystals, these directions coincide) and uniaxial pressure applying. On the basis of this scheme, the forms of extreme surfaces obtained for the investigated crystals are explained.

Exploring the fluorescence action spectrum of photosynthesis

The mathematical study of the fluorescence action spectrum of photosynthesis was performed. The calculation of typical spectra for photosynthesis was done for the red and blue frequencies. The transition of the action spectrum of photosynthesis from wavelengths to the frequency scale was completed. A numerical method based on the use of the inverse Fourier transform approach was used to obtain a relaxation curve for the impulse (time) characteristic of fluorescence. It turned out that the radius vector of the module of impulse response in polar coordinates makes one half-turn or half of the period of light oscillations in time. It was established that the optical medium of a plant during the relaxation time has a negative space charge of electrons, inverse properties and properties of the coherent radiation. The condition of neutrality of the material environment is not met. It was found that the ratio of the variable chlorophyll fluorescence for red and blue light has almost the same value. An analysis of the dependence of the quality factor of the chlorophyll spectrum on frequency shows that the fluorescence energy loss in blue light significantly exceeds the energy loss in red light. The proposed method can be used for express analysis of the intensity of photosynthesis. It was also concluded that plants can emit ultra-wideband signals. The relaxation time of chlorophyll fluorescence is shorter than the relaxation time of electronic polarization in atoms (molecules). As a result, a population inversion is created in the optical medium of chlorophyll - there are more atoms in the upper energy level than in the lower level. Due to this, stimulated emission and amplification of light of the radiative recombination occur. In this case, the emission of fluorescence light becomes coherent. All these properties of plants are considered for the first time and have not been described either in domestic or in foreign articles.

A Novel Method of Jacobian Contours to Evaluate the Influence Line in Statically Determinate Structures

Influence lines are indispensable tools for visualizing and analyzing the dynamic variations in force factors induced by external loads within structural systems. Among these methods, the energetic approach stands as a widely employed technique, rooted in the fundamental principle of work done by changing forces. It enables engineers to transform intricate structural analysis problems into manageable ones by exploring the first derivatives of the radius vector, which represent infinitesimal velocity or displacement. This methodology seamlessly interweaves concepts such as carrier motion, relative motion, and the construction of mechanisms, bringing fresh perspectives to the analysis of influence lines. In this article, we explore the nuances of these novel methods within the domain of mechanism theory. Through comprehensive elaboration and analysis, we elucidate the underlying principles and practical applications of Jacobian contours. Crucially, we introduce a straightforward, rapid, and programmable approach, promising to revolutionize influence line determination in structural engineering. This method bridges the gap between theory and practice, offering the potential to elevate the accuracy, efficiency, and adaptability of influence line analysis. As such, it represents a significant advancement in the field of structural and applied mechanics, with broad-reaching implications for engineering practice.

Constructing geometrical models of spherical analogs of the involute of a circle and cycloid

The common properties of images on a plane and a sphere are considered in the scientific works by scientists-designers of spherical mechanisms. This is due to the fact that the plane and the sphere share common geometric parameters. They include constancy at all points of the Gaussian curve, which has a zero value for a plane and a positive value for a sphere. Figures belonging to them can slide freely on both surfaces. With unlimited growth of the radius of the sphere, its limited section approaches the plane, and the spherical shape transforms into a plane. Thus, a loxodrome that crosses all meridians at a constant angle is transformed into a logarithmic spiral that intersects at a constant angle the radius vectors that come from the pole. The tooth profile of cylindrical gears is outlined by the involute of a circle. A spherical involute is used for the corresponding bevel gears. Other spherical curves are also known, which are analogs of flat ones. The formation of a cycloid and an involute of a circle are associated with the mutual rolling of a line segment with each of these figures. If the segment is fixed and the circle rolls along it, then the point of the circle describes the cycloid. In the case of a stationary circle along which a segment is rolled, the point of the segment will execute the involute. To move to the spherical analogs of these curves, it is necessary to replace the circle with a cone, and the straight line with a plane. The spherical prototype of the cycloid will be the trajectory of the point of the base of the cone, which rolls along the plane, that is, along the sweep of the cone. The sweep of a cone is a sector, the radius of the limiting circle of which is equal to the generating cone. If this sweep, like a section of a plane, is rolled around a fixed cone, when its top coincides with the center of the sector, then the point of the limiting radius of the sector will execute a spherical involute. This paper analytically implements these two motions and reports the parametric equations of the spherical analogs of the circle involute and the cycloid

Experimental Field Tests of the Suitability of a New Seeder for the Soils of Northern Kazakhstan

Kazakhstan is historically a livestock country, and the production of feed requires no less attention than the production of grain. To improve the forage base, one solution is the sowing of high-yielding fodder seeds. An experimental seeder was developed with new design solutions for the sowing machine, with three blades installed at an angle of 120° relative to the lower part of the blower shaft, deviated vertically by 8–10°, along with components with a radius vector of 10–15° and the blower shaft attached to the top of the sowing cylinder. The closing part of the disc coulter contained the press rollers with a disc diameter measuring 350 mm. The field tests were conducted with the parameters between the discs set to α = 10°, a disc vanishing point of β = 40°, a coulter angle of 32°, and an individual 320-mm press roller with a cylindrical 60-mm rim, a leash, and a section for setting the seed placement depth. The wheatgrass varieties “Burabay” and awnless brome “Akmola emerald” were sown. The research showed the higher efficiency of the experimental seeder with seeding units and sowing parts compared to a serial seeder in terms of agricultural performance. The increase in seed germination was 3.56%. The experimental seeder surpassed the regular seeder by 4.95% in terms of the depth uniformity of the seed placement, in terms of yield increase by 5.361 cwt/ha, with reductions in traction resistance of 12.3%, and in fuel consumption by 10%. The economic efficiency from the fuel reduction and yield increase was estimated at around 7700 USD/ha per year.

Комплексная оценка аналитических и численных моделей эфемерид планет Солнечной системы на примере околоземных КА

The paper presents a developed algorithm for using the high-precision numerical ephemerid models. Qualitative and quantitative comparison of analytical and numerical high-precision planetary ephemerid models was carried out, including NASA averaged elements model, Newcomb model, Mees model, DE/LE series models and EPM series models. Absolute values of the radius vector residuals for each planet of the Solar System were obtained within the framework of the considered ephemerid models. Integration methods were evaluated, including Runge—Kutta method of the 4th order, Adams method of the 16th order and Dorman-Prince method of the 5(4)th order. Results of evaluating accuracy and efficiency of calculations depending on the integration stage were obtained. Values of perturbing accelerations from the Sun, Moon and planets for a GLONASS-type spacecraft were calculated. Practical recommendations are provided for using analytical and numerical planetary ephemerides in simulation of the near-Earth spacecraft motion.

Image polar radius distribution for seed orientation adjustment

ABSTRACT Seed orientation is an important factor in high-speed automatic seeders used for sowing crops such as garlic cloves and corn kernels. However, obtaining accurate seed orientation angles can be challenging due to high-frequency noise points and false top features in seed images, which can negatively impact the orientation effect. In this paper, we introduce a directional adjustment method based on the polar radius distribution map to address this issue. Our method involves two main steps. Firstly, we use the morphological opening operation to process speckles and some seed apex parts and use the region marker to obtain the original polar radius distribution curve signal. Secondly, we use the wavelet packet transform to analyze the original polar radius distribution curve signal, which yields a direction rotation angle after analysis and calculation and enables the determination of seed orientation. Our experimental results show that our method can better identify the germination location at the top of the seed, and the calculated rotation angle is more conducive to seed direction adjustment than the rotation angle directly determined by the maximum polar radius in the polar radius vector. This is due to the advantage of higher frequency resolution of wavelet packet analysis, which enables us to obtain a polar radius distribution curve signal with low noise, better smoothness, and more realistic reflection of the edge characteristics of the seed contour boundary. The proposed method provides an effective solution for accurately adjusting the orientation of garlic cloves and corn kernels and potentially other crops that require automation technology. Our key finding is that using the polar radius distribution map and wavelet packet transform can yield better results in seed orientation adjustment, by removing high-frequency noise points and false top features and improving the accuracy of seed rotation angle calculation.

Comparison of Methods for Computing Highly Accurate Daily GNSS Positions

In Central Asia, the level of geodynamic displacements of the Earth's crust does not significantly exceed the accuracy of their measurement methods. Therefore, we need to choose the most accurate methods of calculating coordinates for cosmogeodetic stations. In this work, based on the data of 8 days of GPS measurements at 10 stations, 7 sets of average daily geocentric XYZ coordinates were calculated using different methods. To determine the positions, we used 3 calculation methods in the GAMIT/GLOBK program, 2 methods in the Bernese GNSS software, and 2 web services. To estimate the differences between 7 coordinate sets, we used parameters based on the Euclidean distance between these coordinate samples. The difference analysis of all pair combinations for 7 coordinate sets was carried out by 3D radius vectors, individual coordinate axes, and individual observation stations. The calculations showed that the positioning accuracy and precision depended not only on the coordinate calculation method but also on the selected reference frame. Methods using the international terrestrial reference frame (ITRF) provide station positions with regular deviations of <2 mm and individual deviations up to 5 cm. Methods using the regional and "point" reference frames have regular discrepancies for individual coordinates up to 2 cm and maximum deviations up to 1 m. Converting XYZ coordinates to UVW with the local reference frame reduces the difference between UVW sets by at least 25%. Due to the spatial orientation relative to the studied stations, the X (U) coordinate is reproduced 2-3 times with smaller deviations than other coordinates. The average deviation level of coordinate sets can be an indicator of the quality of conditions for receiving a GNSS signal at one station. We have identified the station group that has a coordinate deviation level several times lower than other stations. Doi: 10.28991/CEJ-2023-09-02-04 Full Text: PDF

THEORETICAL SUBSTANTIATION OF THE RESULTS OF MEASURING ANOMALIES OF SPACECRAFT TRAJECTORIES

It is about the solar acceleration of spacecraft. The prevailing opinion that classical properties of the fundamen¬tal laws of statics can be successfully used in the celestial mechanics of low speeds (v << c) has been refuted because the involvement of relativistic methods does not improve the situation due to the smallness of the gravity mag¬netic acceleration. The essence of the problem is that the known classic methods of the theory of motion operate solely on the transverse component of the velocity vector concerning the orientation of the radius vector of the gravitational interaction. In the article, an insufficient longitudinal component was introduced into the electrogravity theory of motion, the effect of which turned out to be an order of magnitude higher than the effect of the transverse one.

Relativistic hyperbolic motion and its higher order kinematic quantities

We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1 + 3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities.

МОДЕЛЮВАННЯ ГЕОМЕТРІЇ РОТОРА ВАКУУМНОГО НАСОСА РУТС

Mathematical model for designing the surface geometry of the Roots pump rotor based on the Cassini oval principle was derived. The polar coordinate system was used, and the radius vector, the direction of which was set by the φ angle, characterizes the location of the point on the surface of the rotor. The distance of this point from the axis of rotor rotation was set by the calculated value of the ρ_R polar radius vector. The γ angle of rotors rotation characterizes their mutual orientation in the plane of rotation. Peculiarities of the choice of the a and b parameters that satisfy the shape of the rotor surface geometry are considered. An example of rotor geometry is given for rotor radius R = 50 mm, rotor rounding radius r = 20 mm, parameters a = 33.166 and b = 28. Rotor geometry depends on normalized parameters of a and b, which are constant for a given shape of the surface and constructive dimensions. A mathematical model of the usable cross-sectional area of the pump has been developed. The usable cross-sectional area of the pump was simulated by the geometry of the rotors. The area of the rotor was determined by the geometry of the surface, which was described by an elliptic integral of the 2nd kind. The usable cross-sectional area for the given parameters is modelled. The results of simulation in the form of graphical dependences are given. Parameters a and b must meet the condition of √2⁄2<b⁄a<1. Under such conditions, the geometry of the rotor surface will be a Cassini oval. The rotation of the two rotors against each other will be by rolling one surface over another.

МОДЕЛЮВАННЯ ГЕОМЕТРІЇ РОТОРА ВАКУУМНОГО НАСОСА РУТС

Mathematical model for designing the surface geometry of the Roots pump rotor based on the Cassini oval principle was derived. The polar coordinate system was used, and the radius vector, the direction of which was set by the φ angle, characterizes the location of the point on the surface of the rotor. The distance of this point from the axis of rotor rotation was set by the calculated value of the ρ_R polar radius vector. The γ angle of rotors rotation characterizes their mutual orientation in the plane of rotation. Peculiarities of the choice of the a and b parameters that satisfy the shape of the rotor surface geometry are considered. An example of rotor geometry is given for rotor radius R = 50 mm, rotor rounding radius r = 20 mm, parameters a = 33.166 and b = 28. Rotor geometry depends on normalized parameters of a and b, which are constant for a given shape of the surface and constructive dimensions. A mathematical model of the usable cross-sectional area of the pump has been developed. The usable cross-sectional area of the pump was simulated by the geometry of the rotors. The area of the rotor was determined by the geometry of the surface, which was described by an elliptic integral of the 2nd kind. The usable cross-sectional area for the given parameters is modelled. The results of simulation in the form of graphical dependences are given. Parameters a and b must meet the condition of √2⁄2<b⁄a<1. Under such conditions, the geometry of the rotor surface will be a Cassini oval. The rotation of the two rotors against each other will be by rolling one surface over another.

Preimpact Mutual Orbit of the DART Target Binary Asteroid (65803) Didymos Derived from Observations of Mutual Events in 2003–2021

We modeled photometric observations of mutual events (eclipses and occultations) between the components of the binary near-Earth asteroid (65803) Didymos, the target of the Double Asteroid Redirection Test (DART) space mission, which were taken from 2003 to 2021. We derived parameters of the modified Keplerian mutual orbit (allowing for a quadratic drift in the mean anomaly, which is presumably caused by an interplay between the BYORP effect and mutual tides, or by differential Yarkovsky force) of the secondary, called Dimorphos, around the Didymos primary and estimated its diameter. The J2000 ecliptic longitude and latitude of the orbital pole are 320.°6 ± 13.°7 and −78.°6 ± 1.°8, respectively, and the orbital period is 11.921624 ± 0.000018 hr at epoch JD 2,455,873.0 (asterocentric UTC; all quoted uncertainties correspond to 3σ, except the density estimate below). We obtained the quadratic drift of the mean anomaly of 0.15 ± 0.14 deg yr−2. The orbital eccentricity is ≤0.03. We determined the ecliptic longitude and latitude of the radius vector of Dimorphos with respect to Didymos at the nominal time of the DART impact to Dimorphos (JD 2,459,849.46875 geocentric UTC) to be 222.°8 ± 7.°0 and −1.°6 ± 4.°2, respectively. We also estimated the bulk density of the system to be 2.37 ± 0.30 g cm−3 (1σ uncertainty).

Two incompatible types of invariants in the octonion spaces

This paper aims to study some invariants and conservation laws relevant to electromagnetic and gravitational fields by means of the rotational transformations of octonion coordinate systems. The scholars utilize the octonions to analyze the electromagnetic and gravitational fields simultaneously, including the octonion field potential, field strength, field source, linear momentum, angular momentum, torque and force. When the octonion coordinate system transforms rotationally, the vector part of one octonion may alter, while the scalar part of the octonion will remain unchanged. This property allows one to deduce a few invariants, such as the scalar part of octonion radius vector, speed of light, and norm of octonion radius vector. These invariants are the basic postulates for the Galilean transformation and Lorentz transformation. Furthermore, from the rotation transform of octonion coordinate systems, it is capable of deducing several invariants, including the mass, energy and power relevant to gravitational fields, in one octonion space [Formula: see text]. And the term relevant to the electric charge will transform with the rotation of coordinate systems. In another octonion space [Formula: see text], it is capable of inferring a few invariants, including the electric charge related to electromagnetic fields. And the terms relevant to the mass and energy will vary with the rotation of octonion coordinate systems. So, the invariants are divided into two different groups. In particular, the mass conservation law and energy conservation law can be effective simultaneously. But the charge conservation law and mass conservation law are unable to be valid simultaneously, in the strict sense. It is beneficial to further understand the laws of conservation.

Zitterbewegungof massless particles

Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations. Dynamics of the group velocity of a massless particle as a whole and of the corresponding radius vector is determined. This radius vector defines any fixed point of the envelope of the moving wave packet characterizing the particle and its group velocity differs from the group velocities of any points of the wavefront. We consider free massless scalar and Dirac particles, the photon, and massive and massless particles with an arbitrary spin and describe them in different representations. For particles with an arbitrary spin, the generalized Feshbach-Villars representation and the Foldy-Wouthuysen one are used. Zitterbewegung takes place in any representation except for the Foldy-Wouthuysen one. Formulas describing the motion of a ``trembling'' free particle are the same in any representation. In the Foldy-Wouthuysen representation, the operators of the velocity and momentum of a free particle are proportional and Zitterbewegung does not take place. Since the radius vector (position) and velocity operators are the quantum-mechanical counterparts of the classical position and velocity just in the Foldy-Wouthuysen representation, Zitterbewegung is not observable. The same conclusion has been previously made for free massive particles. For relativistic massive particles with spins 0, 1/2, 1 and massless particles with spins 0, 1/2 in arbitrarily strong electromagnetic fields, independent of the external fields Zitterbewegung does not appear in the Foldy-Wouthuysen representation either. This conclusion is made for leading terms in the Hamiltonian proportional to the zero and first powers of the Planck constant and for such terms proportional to ${\ensuremath{\hbar}}^{2}$ which describe contact interactions.

Accounting for the Yarkovsky Effect in Reference Frames Associated with the Radius Vector and Velocity Vector

Accounting for the Yarkovsky Effect in Reference Frames Associated with the Radius Vector and Velocity Vector