Hybrid Coordinate System Research Articles

An Efficient Image Reconstruction Algorithm for Maneuvering Platform SAR Integrated With Elevation Information in Hybrid Coordinate System

An Efficient Image Reconstruction Algorithm for Maneuvering Platform SAR Integrated With Elevation Information in Hybrid Coordinate System

Black holes in the theory of the dynamic medium of reference

The aim of this article is to apply the theory of the dynamic medium of reference [O. Pignard, Phys. Essays 32, 422 (2019)] to black holes and to find all the results of general relativity concerning black holes without rotation and without load. Among the most important results to which this article leads, we can mention: (1) The speed of the flux of the medium is greater than the speed of light inside the horizon of a black hole or even much greater than the speed of light at a distance from the center of the black hole much less than the radius of Schwarzschild. (2) In the hybrid coordinate system (drSchwarzschild, dtfree fall), the speed of light is established simply in relation to its propagation medium. (3) A photon emitted at an infinite distance from the black hole with speed c 0 arrives near the horizon of the black hole with a real speed zero. And yet the local measurement of the speed of the photon carried out with a material clock and a material ruler remains c 0. (4) Study of the possible orbits of a material particle around a black hole and the possibility of orbits of a photon around a black hole.

A Fast Time-Domain SAR Imaging and Corresponding Autofocus Method Based on Hybrid Coordinate System

Compared with frequency-domain algorithms, time-domain algorithms (TDAs) can achieve image focusing under the conditions of arbitrary trajectories and large integration angles. However, the interpolations in both range and bearing angle directions are required in the coordinate transformation of fast TDAs, which inevitably increases the computational load and introduces interpolation errors. In this paper, a fast time-domain imaging and corresponding autofocus method based on the hybrid coordinate (HC) system is proposed. First, the interpolation operation is optimized in the process of fast TDAs. It transforms the 2-D interpolation into 1-D interpolation only in the bearing angle direction, which improves the execution efficiency and reduces the interpolation error. Next, a 3-D trajectory deviation estimation method based on Gauss–Newton iteration is investigated for the motion compensation in the HC system. By iterative optimization, the 3-D motion errors during the flight are estimated accurately, and the space-variant phase error is compensated precisely. This method has good robustness and universality. Simulation results and real data processing demonstrate the effectiveness and the practicability of the method presented in this paper.

Generalized Lagrange’s equations for systems with general constraints and distributed parameters

This paper presents a general explicit differential form of Lagrange’s equations for systems with hybrid coordinates and general holonomic and nonholonomic constraints. The appropriate constraint conditions are imposed on d’Alembert–Lagrange principle via Lagrange multipliers to find the correct equations of state of nonholonomic systems. The developed equations take the differential form in terms of the Lagrangian, accounting for the masses and springs that may exist at the boundary. The Lagrangian of hybrid-coordinate systems consists of three parts: the first is due to the rigid-body motion, the second is due to the boundary elements, and the third is the Lagrangian density due to the elastic elements. The developed Lagrange’s equations produce the equations of state and the boundary conditions without the need to carry out the integration by parts generally one needs to do using Hamilton’s principle. Illustrative examples are introduced to show the effectiveness of the developed equations.

Inflying perspectives of reduced phase space

There is widespread disagreement about how the general covariance of a theory affects its quantization. Without a complete quantum theory of gravity, one can examine quantum consequences of coordinate choices only in highly idealized `toy' models. In this work, we extend our previous analysis of a self-gravitating shell model [1], and demonstrate that coordinate freedom can be retained in a reduced phase space description of the system. We first consider a family of coordinate systems discussed by Martel and Poisson [2], which have time coordinates that coincide with the proper times of ingoing and outgoing geodesics (for concreteness, we only consider the former). Included in this family are Painlev\'e-Gullstrand coordinates, related to a network of infalling observers that are asymptotically at rest, and Eddington-Finkelstein coordinates, related to a network of infalling observers that travel at the speed of light. We then introduce "inflying" coordinates - a hybrid coordinate system that allows the infalling observers to be arbitrarily boosted from one member of the aforementioned family to another. We perform a phase space reduction using inflying coordinates with an unspecified boosting function, resulting in a reduced theory with residual coordinate freedom. Finally, we discuss quantization, and comment on the utility of the reduced system for the study of coordinate effects and the role of observers in quantum gravity.

Co-Design of Strain-Actuated Solar Arrays for Spacecraft Precision Pointing and Jitter Reduction

This work presents a novel spacecraft attitude control architecture using strain-actuated solar arrays that does not require the use of conventional attitude control hardware. A strain-actuated solar array enables attitude slewing maneuvers and precision pointing (image acquisition) stares, while simultaneously suppressing structural vibrations. Distributed piezoelectric actuators help achieve higher precision, higher bandwidth, and quieter operation than reaction wheels. To understand the design tradeoffs for this architecture, a framework for the integrated design of distributed structural geometry and distributed control is presented. The physical properties of the array are modeled and designed with respect to a piecewise linear distributed thickness profile. The distributed control is a voltage profile across the array modeled as a spatially continuous function. The dynamics of the system are modeled using a coupled ordinary differential equation–partial differential equation system using extended generalizations for hybrid coordinate systems. The combined physical and control system design, or co-design problem is investigated to understand the optimal performance of the system. Single-axis slew maneuvers of 7.2 milliradians or 1485 arcsec are achieved for a representative spacecraft model without increasing array mass or reducing array planform area. From additional tradeoff studies, a design criteria is revealed for the array structure and control strategy based on the optimal design tradeoff between large array inertia and fast structural dynamics. Moreover, the fundamental limits on strain-actuated solar arrays slew angle magnitude are demonstrated using an intuitive pseudorigid body dynamic model.

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method.

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double-ended and single-ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image-nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single-ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended-growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen-transfer and ligand-exchange events, while formation of H-bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter) is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton's second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM) are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

Modeling of the lower ionosphere climate

A coupled model of the troposphere-stratosphere-mesosphere and the ionospheric D region (for 0–90 km altitudes) is presented. The model is based on a three-dimensional general atmospheric circulation model in a hybrid coordinate system. A five-component model has been taken as a photochemical model for the lower ionosphere. The role of the neutral atmosphere thermodynamic characteristics in the formation of the D layer mean state has been investigated by the model results. Based on a preliminary model identification using direct measurements, and radiowave absorption and propagation, it has been indicated that the model satisfactorily reproduces climatic characteristics of the ionospheric D layer.

Study on a New Algorithm for Tracking Ballistic Missile in Free Flight Phase

This paper presents an application of a new adaptive filtering algorithm based on a standard earth ellipsoid model in tracking ballistic missile in free flight phase. The traditional Extended Kalman Filtering algorithm (EKF) has defect in two aspects: 1) observation values applied in observation equation mainly include azimuth, pitch angle and radial distance (or radial velocity), without Doppler frequency; 2) Jacobi matrix of the system needs to be calculated, and high nonlinearization could result in degradation of calculation precision. In this paper, an algorithm used for tracking ballistic missile in free flight phase which is based on UKF observation equation with Doppler frequency is presented. The algorithm has been applied in hybrid coordinate system of the standard earth ellipsoid model (the earth is assumed as an ellipsoid planet). It has higher tracking precision compared with EKF algorithm. Monte Carlo simulation conducted to model ballistic missile in free flight phase by using MATLAB software justified the efficacy and the reasonableness of the new algorithm.

The Hybrid Coordinate Measurement System as a Response to Industrial Requirements

The Hybrid Coordinate Measurement System as a Response to Industrial RequirementsThe tendencies of modern industry are to increase the quality of manufactured products, simultaneously decreasing production time and cost. The hybrid system combines advantages of the high accuracy of contact CMM and the high measurement speed of non-contact structured light optical techniques. The article describes elements of a developed system together with the steps of the measurement process of the hybrid system, with emphasis on segmentation algorithms. Additionally, accuracy determination of such a system realized with the help of a specially designed ball-plate measurement standard is presented.

Hybrid State Plane Coordinate System for Transforming a Citywide Survey Control Network to Surface Values: Case Study for Frisco, Texas

The city of Frisco, Tex., published state plane coordinates were “ground scaled” into surface coordinates for the purpose of establishing a hybrid coordinate system to be easily used by surveyors. Nineteen city monuments were found and collected by GPS observation using real-time kinematic (RTK) connected to the Texas RTK Cooperative Network. The network creates a virtual reference station near the GPS roving receiver, allowing the surveyor to use the rover unit by itself without the need for setting up a base station on the project site. Using a GPS manufacturer’s standard protocol, localizing ground-scaled GPS vectors to the city’s hybrid values yielded acceptable horizontal (H) and vertical (V) residuals over a 233 km2 network. Two out of 19 monuments observed explained maximum residual error ( H=0.029 m , V=0.082 m ) with no significant differences in the mean ΔN and ΔE between published grid, hybrid, and surface coordinates (P=0.77) . This paper will illustrate and discuss the procedures and results ...

A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM)

A hierarchy of one-dimensional high-order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated. The schemes are also compared based on remapping experiments in closed domains. The piecewise quartic method (PQM) is presented, based on fifth-order accurate piecewise polynomials, and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models, which require the remapping to be conservative, monotonic and highly accurate. A limiter for this scheme is fully described that never decreases the polynomial degree, except at the location of extrema. We assess the use of high-order explicit and implicit (i.e., compact) estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method (PPM) and PQM. It is shown that all limited PQM schemes perform significantly better than limited PPM schemes and that PQM schemes are much more cost-effective.

복합좌표계 시스템의 선회동역학에 관한 해석적 연구

본 논문에서는 선회모드와 구조모드를 가지는 복합좌표계 시스템의 선회동역학을 시간유한요소법을 이용하여 전개할 때에 발생하는 수치적 문제점을 극복할 수 있는 해석적 해법을 제안하였다. 시간유한요소법을 이용한 복합좌표계 시스템의 동역학은 선회모드와 구조모드가 서로 연성된 두 개의 행렬미분방정식으로 전개될 수 있음을 보였다. 공간전파관계식을 시간영역 모드좌표계로 변환하고, 각 시간모드에 대한 해석적 공간전파관계식을 유도하였다. 경계조건의 적용을 통해 선회각에 대한 해석적 관계식을 구하였으며, 이를 이용함으로써 각 모드에 대한 공간 특성치를 구하였다. 수치 예제를 통하여 기존의 상태천이행렬을 이용한 해법과 비교함으로써 제안된 해석적 해법을 타당성을 검증하였다. In this paper, an analytic solution method is proposed to overcome the numerical problems when the slewing dynamics of hybrid coordinate systems is investigated via time finite element analysis. It is shown that the dynamics of the hybrid coordinate systems is governed by the coupled dual differential equations for both slewing and structural modes. Structural modes are transformed into the time-based modal coordinates and analytic spatial propagation equations are derived for each space-dependent time mode. Slew angle history is obtained analytically by appropriate applications of the boundary conditions and structural propagation is re-calculated using the slew angle. Numerical examples are demonstrated to validate the proposed analytic method in comparison to the existing state transition matrix method.

The Scalable Modeling System: directive-based code parallelization for distributed and shared memory computers

A directive-based parallelization tool called the Scalable Modeling System (SMS) is described. The user inserts directives in the form of comments into existing Fortran code. SMS translates the code and directives into a parallel version that runs efficiently on shared and distributed memory high-performance computing platforms including the SGI Origin, IBM SP2, Cray T3E, Sun, and Alpha and Intel clusters. Twenty directives are available to support operations including array re-declarations, inter-process communications, loop translations, and parallel I/O operations. SMS also provides tools to support incremental parallelization and debugging that significantly reduces code parallelization time from months to weeks of effort. SMS is intended for applications using regular structured grids that are solved using finite difference approximation or spectral methods. It has been used to parallelize 10 atmospheric and oceanic models, but the tool is sufficiently general that it can be applied to other structured grids codes. Recent performance comparisons demonstrate that the Eta, Hybrid Coordinate Ocean model and Regional Ocean Modeling System model, parallelized using SMS, perform as well or better than their OpenMP or Message Passing Interface counterparts.

A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models

Most numerical weather prediction models rely on a terrain-following coordinate framework. The computational mesh is thus characterized by inhomogeneities with scales determined by the underlying topography. Such inhomogeneities may affect the truncation error of numerical schemes. In this study, a new class of terrainfollowing coordinate systems for use in atmospheric prediction models is proposed. Unlike conventional systems, the new smooth level vertical (SLEVE) coordinate yields smooth coordinates at mid- and upper levels. The basic concept of the new coordinate is to employ a scale-dependent vertical decay of underlying terrain features. The decay rate is selected such that small-scale topographic variations decay much faster with height than their large-scale counterparts. This generalization implies a nonlocal coordinate transformation. The new coordinate is tested and compared against standard sigma and hybrid coordinate systems using an idealized advection test. It is demonstrated that the presence of coordinate transformations induces substantial truncation errors. These are critical for grid inhomogeneities with wavelengths smaller than approximately eight grid increments, and may overpower the regular-grid truncation error of the underlying finite-difference approximation. These results are confirmed by a theoretical analysis of the truncation error. In addition, the new coordinate is tested in idealized and real-case numerical experiments using a nonhydrostatic model. The simulations using the new coordinate yield a substantial reduction of small-scale noise in dynamical and thermodynamical model fields.

MODELLING OF VIBRATING SYSTEMS USING TIME-DOMAIN FINITE ELEMENT METHOD

In this paper, several dynamic systems are modelled using the time-domain finite element method. Galerkin's weak principle is used to model the general second order mechanical system, and is applied to the dynamics of the simple pendulum. Problems that arise during the approximation of the final momentum are also investigated. Furthermore, additional dynamic analysis methods are suggested for hybrid co-ordinate systems that have both slew and flexible modes. The proposed methods are based on both extended Hamilton's principle and Galerkin's weak principle. The matrix wave equation is propagated in a space domain, satisfying the geometric/natural boundary conditions. As a result, the flexible motion can be obtained, and this was compatible with the applied control input. A numerical example is used to demonstrate the effectiveness of the proposed modelling methods for the hybrid co-ordinate systems.

A Pathological Problem with NCEP Reanalyses in the Stratosphere

A pathological problem has been discovered in the NCEP reanalyses in the stratosphere. It is manifested most strongly as a two-delta vertical wave in the divergence of the wind field above steep topography especially where the wind increases with altitude in the stratosphere. It is present primarily above 50 mb at the topmost four levels in the NCEP model used for data assimilation and appears to be directly related to the use of the sigma (terrain following) coordinate system and the upper boundary condition in the assimilating model. Recommendations suggested for addressing the problem include switching to a hybrid coordinate system that transitions to a pressure coordinate in the stratosphere, and with a damping upper boundary condition. Certain climate diagnostics are greatly impacted by these pathologies.

Non-Cartesian coordinates for instantaneous normal mode theory of atomic liquids

A hybrid coordinate system of spherical polar coordinates for the mutual nearest-neighbor pairs and Cartesian coordinates for the unpaired atoms is introduced for instantaneous normal mode (INM) analysis of atomic liquids. Densities of states (dos) calculated with the hybrid coordinates in a unit-density, supercooled Lennard-Jones liquid differ from those obtained with Cartesian coordinates, primarily at imaginary frequency. A brief discussion of coordinate dependence is presented, with an analytic treatment of the frequency moments, and it is argued that the hybrid dos are more physically meaningful. INM theory strives to relate Im ω modes to diffusion and barrier crossing, but spurious nondiffusive contributions must be removed. Hybrid coordinates yield substantially fewer Im ω indicating that some nondiffusive modes are simply Cartesian artifacts. Normalized hybrid and Cartesian Re ω dos are nearly identical, as are velocity correlation functions C(t) obtained by treating the Re ω INM as a complete set of harmonic modes. These C(t) are in fair agreement with simulation, but, notably, reach an insufficiently deep negative minimum value at too short a time. A harmonic approximation using the hybrid-translational Re ω dos, in which the hybrid modes are projected onto the center-of-mass translations of the mutual neighbor pairs plus the unpaired atoms, yields much better agreement.

Maneuver and vibration control of hybrid coordinate systems using Lyapunov stability theory

In this study, we present a generalized control law design methodology that covers a large class of systems, especially flexible structures described by hybrid discrete/distributed coordinate systems. The Lyapunov stability theory is used to develop globally stabilizing control laws. A hybrid version of Hamilton's canonical equations is introduced, which provides a direct path to designing stabilizing control laws for general nonlinear hybrid systems. The usual loss of robustness due to model reduction is overcome by this Lyapunov approach, which does not require truncation of the flexible systems into finite dimensional discrete systems.