Multiple Systems for Spatial Imagery: Transformations of Objects and Bodies

Problem-solving often requires imagining spatial changes. Object-based transformations allow imagining an object in a different orientation. Perspective transformations allow imagining changes in one's viewpoint. Three experiments tested the hypothesis that these two transformations are dissociable and specialized for different situations, by manipulating instructions and task parameters and measuring response times, errors, and introspective reports. Human experience with small objects such as telephones and clothes irons consists mostly of manipulation or observed manipulation, which is characterized by object-based transformations. Consistent with this experience, when participants made judgments about small manipulable objects, they showed a strong tendency to use object-based transformations. Experience with human bodies is more varied, including both object-like interactions and interactions in which one must estimate another's perspective. Accordingly, when making judgments about pictures of bodies, participants' selection of a spatial transformation depended on the type of judgment that needed to be made. When instructions violated these natural mappings, performance was impaired. These data argue for the view that multiple spatial transformation systems evolved to solve different spatial reasoning problems.     

空间可展开结构拓扑综合方法研究

空间可展开结构的构型用邻接矩阵表示,采用拓扑变换的方法来研究空间可展开结构 的拓扑综合。通过构件的增加、减少以及连接关系变化的变胞综合方法实现不同构型之间的 变换运算。以周边桁架可展开天线结构为例,通过构型变换,得到了不同于目前同步展开／ 收拢方式的混合展开收拢方式,以及新的可展开结构的构型。通过所得类型的运动仿真,表 明了混合展开方式以及新的可展开结构类型的可行性,验证了空间可展开结构拓扑综合的变 胞综合方法。     

Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

某卫星不同受力环境下精度测试方法的新思路

文章简要介绍了卫星精度测试过程中不同受力（包括空载、满载、充气、不充气）环境下所采取的一些新的精测思路,并通过具体的分析和计算,确定了不同的精测方法和步骤,其中涉及多基准的建立、转换及变形量的补偿等。共使用了７块立方镜、建立了4个基准,分步解决了卫星重力变形、卫星充气变形对精度造成的影响,满足该卫星的总装精度测量要求。     

Expert Algorithmic and Imagistic Problem Solving Strategies in Advanced Chemistry

Abstract

Visualization and imagistic reasoning appear central to expert practice in science; however, expert use of these strategies on authentic tasks has not been examined in detail. This study documents how science experts use both algorithms and imagistic reasoning to solve problems. Using protocol analysis, we report expert chemists' preferential use of algorithms for solving spatial problems and imagistic reasoning for deducing spatial transformations. We observed experts employ algorithms to solve the majority of spatial tasks while reserving imagistic strategies to solve a class of tasks that required translating between representations. Strategy used varied widely among experts and tasks.     

Organization of the on-ground data processing for remote sensing purposes using finite rings and fields concept

In most of the modern on-ground data processing systems for remote sensing the digital signal conversions, on the analogy of the analog signal, are defined over a field of complex numbers, C, as the digital signal values (as well as those of the analog one) may be regarded as a subset of the field. Such an approach requires substantial computing and hardware expenses. For a signal defined in the finite range N (N = 0, 1, …, n − 1) most of the algorithms require the number of operations proportional to log N, N, N² and even to greater powers of N. That is why the building up of the data processing system mathematical model with a minute number of computations, as well as the computations organization, is a problem of great importance. It is not always necessary to build up a model using transformations over the field C. These transformations may be also defined over some other (abstract) fields, e.g. over the finite field GF(p) or finite residue ring moduli M, Z_M. This approach gives numerous advantages. They are discussed in the presented paper along with limitations of the approach. A series of the data processing system models are described. The design concepts for the on-ground images processing equipment are also discussed.     

Preferred and Alternative Mental Models in Spatial Reasoning

The mental model theory postulates that spatial reasoning relies on the construction, inspection, and the variation of mental models. Experiment 1 shows that in reasoning problems with multiple solutions, reasoners construct only a single model that is preferred over others. Experiment 2 shows that inferences conforming to these preferred mental models (PMM) are easier than inferences that are valid for alternatives. Experiments 3 and 4 support the idea that model variation consists of a model revision process. The process usually starts with the PMM and then constructs alternative models by local transformations. Models which are difficult to reach are more likely to be neglected than models which are only minor revisions of the PMM.     

Approximate solutions to minimax optimal control problems for aeroassisted orbital transfer

This paper considers minimax problems of optimal control arising in the study of aeroassisted orbital transfer. The maneuver considered involves the coplanar transfer from a high planetary orbit to a low planetary orbit. An example is the HEO-to-LEO transfer of a spacecraft, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit.The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by means of lift modulation. The presence of upper and lower bounds on the lift coefficient is considered.The following minimax problems of optimal control are investigated: (i) minimize the peak heating rate, problem P1; and (ii) minimize the peak dynamic pressure, problem P2. It is shown that problems P1 and P2 are approximately equivalent to the following minimax problem of optimal control: (iii) minimize the peak altitude drop occurring in the atmospheric portion of the trajectory, problem P3.Problems P1–P3 are Chebyshev problems of optimal control, which can be converted into Bolza problems by suitable transformations. However, the need for these transformations can be bypassed if one reformulates problem P3 as a two-subarc problem of optimal control, in which the first subarc connects the initial point and the point where the path inclination is zero, and the second subarc connects the point where the path inclination is zero and the final point: (iv) minimize the altitude drop achieved at the point of junction between the first subarc and the second subarc, problem P4. Note that problem P4 is a Bolza problem of optimal control.Numerical solutions for problems P1–P4 are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed. In particular, it is shown that, from an engineering point of view, it is desirable to solve problem P3 or P4, rather than problems P1 and P2.     

Hori method for generalized canonical systems

In this paper, some special features on the canonical version of Hori method, when it is applied to generalized canonical systems (systems of differential equations described by a Hamiltonian function linear in the momenta), are presented. Two different procedures, based on a new approach for the integration theory recently presented for the canonical version, are proposed for determining the new Hamiltonian and the generating function for systems whose differential equations for the coordinates describe a periodic system with one fast phase. These procedures are equivalent and they are directly related to the canonical transformations defined by the general solution of the integrable kernel of the Hamiltonian. They provide the same near-identity transformation for the coordinates obtained through the non-canonical version of Hori method. It is also shown that these procedures are connected to the classic averaging principle through a canonical transformation. As examples, asymptotic solutions of a non-linear oscillations problem and of the elliptic perturbed problem are discussed.     

Quaternion regularization in celestial mechanics and astrodynamics and trajectory motion control. I

Regularization problems in celestial mechanics and astrodynamics are considered. The fundamental regular quaternion models of celestial mechanics and astrodynamics are presented. It is shown that the efficiency of analytical investigation and numerical solution of boundary problems of optimal trajectory motion control of spacecraft may be increased using quaternion astrodynamics models. The regularization problem of celestial mechanics and astrodynamics that implies eliminating the feature, which arises in the equations of the two-body problem in case of impact of the second body with the central body, is considered in the first section of the paper. The quaternion method for regularizing the equations of the perturbed spatial two-body problem suggested by the author is presented; the method is compared with Kustaanheimo-Stiefel (KS) regularization. Demonstrative geometric and kinematic interpretations of regularizing transformations are provided. Regular quaternion equations for the two-body problem, which generalize the regular Kustaanheimo-Stiefel equations, as well as regular equations in quaternion osculating elements and quaternion regular equations for perturbed central motion of a material point, are considered. The papers on quaternion regularization in celestial mechanics and astrodynamics are briefly analyzed.     

论空间环境模拟试验和研究

文章介绍了空间环境模拟技术的发展及空间环境效应的防护,并提出了空间环境研究理念的几个应注意的重要的转变.     

天基照相跟踪空间碎片批处理轨道确定研究

随着国内外天基观测空间碎片研究的展开,文章提出了利用跟踪卫星的CCD(Charge
Coupled Device)相机对空间碎片进行轨道探测的方法,首先建立了CCD照相观测模型和基于 照相观测 的空间碎片批处理轨道确定模型。通过对CCD相机底片归算方法的分析可知,利用
CCD相机所获得的观测数据与跟踪卫星的姿态无关,且其精度只与测量和坐标转换计算的精 度有关,在测量和计算中可获得较高的精度。分别对分布密度较高的低轨道和地球同步 轨道区域的空间碎片进行了定轨分析。仿真结果表明,定轨时采用两个跟踪弧段的照相数据 定轨精度大大高于一个弧段照相数据的定轨精度;跟踪卫星距离空间碎片越近,定轨精度越 高;低轨道空间碎片的定轨精度高于地球同步轨道上的空间碎片定轨精度。
     

一种非线性最优导弹制导律

以质点飞行器的非线性运动方程为基础，研究了导弹拦截目标问题。运用线化变换理论和线性二次型微分对策理论，导出了导弹和目标的最优控制策略，对导弹最优策略进行了综合分析，给出了一种可以实时实现的最优制导律。并以某型中远程地－空导弹的气动数据和数学模型为基础，进行了全弹道拦截数字仿真，仿真结果表明：该制导律在减少终端脱靶量方面比空间比例导引的效果好。     

Closed form perturbation solution of a fast rotating triaxial satellite under gravity-gradient torque

The attitude dynamics of a fast rotating triaxial satellite under gravity-gradient is revisited. The essentially unique reduction of the Euler-Poinsot Hamiltonian, which can be performed in different sets of variables, provides a suitable set of canonical variables that expedites the perturbation approach. Two canonical transformations reduce the perturbed problem to its secular terms. The secular Hamiltonian and the transformation equations of the averaging are computed in closed form of the triaxiality coefficient, thus being valid for any triaxial body. The solution depends on Jacobi elliptic functions and integrals, and applies to non-resonant rotations under the assumption that the rotation rate is much higher than the orbital or precessional motion.     

Transformations and representations supporting spatial perspective taking

Spatial perspective taking is the ability to reason about spatial relations relative to another’s viewpoint. Here, we propose a mechanistic hypothesis that relates mental representations of one’s viewpoint to the transformations used for spatial perspective taking. We test this hypothesis using a novel behavioral paradigm that assays patterns of response time and variation in those patterns across people. The results support the hypothesis that people maintain a schematic representation of the space around their body, update that representation to take another’s perspective, and thereby to reason about the space around their body. This is a powerful computational mechanism that can support imitation, coordination of behavior, and observational learning.     

Variational equations in parametric variables and transformation of their solutions

An analytical relationship is derived which connects the matrix of partial derivatives of the current state vector with respect to the initial conditions with the matrix of solutions to variational equations in parametric variables. These equations correspond to the equations of motion obtained using the generalized coordinate-time transformation admitting an increase of the number of unknown parameters. Particular cases of transformations leading to the variational equations in regularizing variables of Sperling-Burdet and Kustaancheimo-Stiefel are considered. All formulas necessary in these cases for determination of the matrix of isochronous derivatives are obtained.     

The cognitive adequacy of Allen's interval calculus for qualitative spatial representation and reasoning

Qualitative spatial reasoning (QSR) is often claimed to be cognitively more plausible than conventional numerical approaches to spatial reasoning, because it copes with the indeterminacy of spatial data and allows inferences based on incomplete spatial knowledge. The paper reports experimental results concerning the cognitive adequacy of an important approach used in QSR, namely the spatial interpretation of the interval calculus introduced by Allen (1983). Knauff, Rauh and Schlieder (1995) distinguished between the conceptual and inferential cognitive adequacy of Allen's interval calculus. The former refers to the thirteen base relations as a representational system and the latter to the compositions of these relations as a tool for reasoning. The results of two memory experiments on conceptual adequacy show that people use ordinal information similar to the interval relations when representing and remembering spatial arrangements. Furthermore, symmetry transformations on the interval relations were found to be responsible for most of the errors, whereas conceptualneighborhood theory did not appear to correspond to cognitively relevant concepts. Inferential adequacy was investigated by two reasoning experiments and the results show that in inference tasks where the number of possible interval relations for the composition is more than one, subjects ignore numerous possibilities and interindividually prefer the same relations. Reorientations and transpositions operating on the relations seem to be important for reasoning performance as well, whereas conceptual neighborhood did not appear to affect the difficulty of reasoning tasks based on the interval relations.     

The Use of Quaternions in the Optimal Control Problems of Motion of the Center of Mass of a Spacecraft in a Newtonian Gravitational Field: I

The problem of optimal control is considered for the motion of the center of mass of a spacecraft in a central Newtonian gravitational field. For solving the problem, two variants of the equations of motion for the spacecraft center of mass are used, written in rotating coordinate systems. Both the variants have a quaternion variable among the phase variables. In the first variant this variable characterizes the orientation of an instantaneous orbit of the spacecraft and (simultaneously) the spacecraft location in this orbit, while in the second variant only the instantaneous orbit orientation is specified by it. The suggested equations are convenient in the respect that they allow the general three-dimensional problem of optimal control by the motion of the spacecraft center of mass to be considered as a composition of two interrelated problems. In the first variant these problems are (1) the problem of control of the shape and size of the spacecraft orbit and (2) the problem of control of the orientation of a spacecraft orbit and the spacecraft location in this orbit. The second variant treats (1) the problem of control of the shape and size of the spacecraft orbit and the orbit location of the spacecraft and (2) the problem of control of the orientation of the spacecraft orbit. The use of quaternion variables makes this consideration most efficient. The problem of optimal control is solved on the basis of the maximum principle. Several first integrals of the systems of equations of the boundary value problems of the maximum principle are found. Transformations are suggested that reduce the dimensions of the systems of differential equations of boundary value problems (without complicating them). Geometrical interpretations are given to the transformations and first integrals. The relation of the vectorial first integral of one of the derived systems of equations (which is an analog of the well-known vectorial first integral of the studied problem of optimal control) with the found quaternion first integral is considered. In this paper, which is the first part of the work, we consider the models of motion of the spacecraft center of mass that employ quaternion variables. The problem of optimal control by the motion of the spacecraft center of mass is investigated on the basis of the first variant of equations of motion. An example of a numerical solution of the problem is given.