Description Of Relative Motion Research Articles

Relative Lagrangian Formulation of Finite Thermoelasticity

The motion of a body can be expressed relative to the present configuration of the body, known as the relative motion description, besides the classical Lagrangian and the Eulerian descriptions. When the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system of boundary value problems becomes linear. This formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. This article presents these ideas applied to thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Some applications of such a formulation in numerical simulations are briefly reviewed and a numerical result is shown.

Colloidal mushy layers

Abstract

Satellite Relative Motion Modeling and Estimation via Nodal Elements

In this paper, a new parameterization of the relative motion between two satellites orbiting a central body is presented. The parameterization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the relative line of nodes. These are combined with classical orbital elements to yield a nonsingular relative motion description. The exact nonlinear, perturbed dynamic model resulting from the new parameterization is established. The proposed parameter set captures the fundamental Keplerian invariants, while retaining a simple relationship with local orbital coordinates. An angles-only relative navigation filter and a collision avoidance scheme are devised by exploiting these features. The navigation solution is validated on a case study of an asteroid flyby mission. It is shown that a collision can be detected early on in the estimation process, which allows one to issue a timely evasive maneuver.

Modeling of washout of a well-killing liquid after launching of an oil well

The paper presents the results of mathematical modeling of the process of launching and output to the mode of an oil well, which was uploaded by a well-killing liquid at the stage of repairs. After the launching of the electric submergible pump the drop of the bottomhole pressure occurs and the inflow of reservoir fluid begins. As a result the multicomponent mixture is generated inside the well, which consists of oil, associated water, well-killing liquid and free gas, originated from the oil during degassing, and this mixture is pumped out towards wellhead. As soon as the pump characteristics are changed, when the liquid with variable density is pumped out, it is necessary to control the speed of a shaft of the pump for providing the stable pump regime. This problem is solved in the paper for different ratios of densities of well-killing liquid and reservoir fluid by the mathematical modeling of multiphase flow in the well elements and inside the pump. As a mathematical model the one-dimensional quasi-stationary model in approach of drift for description of relative motion of the components is applied, which proved itself well for modeling of non-stationary processes lasting for several days. The comparison of calculated and measuring field parameters is presented. It is shown that the speed of washout of the well-killing liquid from the oil well and the probability of the pump stop due to its head failure depend on the ration of densities of the well-killing liquid and reservoir fluid. It is stated that the monitoring of change of parameters of the pump in time through the mathematical modeling can help to optimize the output to the mode of the well. This allows to avoid stops due to the pump head failure and to diminish the electricity costs.

Newton’s Bucket Experiment from Kantian Perspective

Newton’s absolute pace-time view is the basis of his classical mechanics, and his description of relative motion is based on absolute space. However, the existence of this absolute space has been questioned by the academic circles. In order to defend its theoretical foundation, Newton established a famous bucket experiment to prove the existence of absolute space. But his experiment was also questioned, and the experiment is also divided into different opinions. This paper hopes to find the answer to the question from Kantian perspective.

Optimal Continuous-Thrust Rephasing Maneuver in Circular Orbit

The minimum-time constant-thrust circular orbit rephasing problem is studied using a curvilinear relative motion description for dynamics. The resulting optimal control problem in the thrust orientation is formulated using the indirect method and investigated both analytically and numerically. By linearizing the relative motion equations, a key nondimensional parameter is identified, which characterizes the duration of the maneuver and its qualitative structure when changing from a short-maneuver to a long-maneuver time regime, passing through a transition zone. Approximate analytical solutions are obtained for the short- and long-maneuver regimes, providing an accurate estimation of the minimum maneuver time and a clear understanding of the evolution of the optimal thrust profile, which approaches two opposite bang–bang structures in the limit cases. The nonlinear problem is investigated numerically and shown to be fully characterized by two nondimensional parameters instead of one. Finally, a comparison with different two-impulse maneuvers is conducted. The results can be used for constructing good initial guesses in more complex optimization problems and to support preliminary mission design.

Successive Linear Approximation for Large Deformation—Instability of Salt Migration

In continuum mechanics, concerning the motion of a body, besides the Lagrangian and the Eulerian descriptions, the description relative to the present configuration of the body instead of the fixed reference configuration has been known as the relative motion description. Although the relative motion description is mostly ignored in the formulation of boundary value problems, it is interesting to consider such a formulation for problems in general for solid bodies. In doing so, there is an advantage that when the time increment from the present state is small enough, the nonlinear constitutive equation can be linearized relative to the present configuration, so that the resulting boundary value problem becomes linear. We can then propose a linear algorithm for large deformation, by building up successive small incremental deformation problem at every time step in the deformation process. In fact, the proposed method is a process of repeated applications of the well-known “small deformation superposed on finite deformation” in the literature. As an application of the proposed numerical method, we consider instability of a two-layered solid body of a denser material on top of a lighter one. This problem is widely known to geoscientist in sediment-salt migration as salt diapirism. In the literature, this problem has often been treated as Rayleigh–Taylor instability in viscous fluids instead of solid bodies. As an example, we propose a viscoelastic solid material model from constitutive theories of continuum mechanics, and present results of numerical simulations of sediment-salt migration which exhibit some main characteristics of salt diapirism as observed by geophysicists.

Modelling dynamics of certain class of discrete multi-body systems based on direct method of the dynamics of relative motion

The paper presents the author’s method of numerical modelling multi-body systems of a rail vehicle class. The method exploits dynamics of relative motion, which describes perturbations in general motion of the vehicle. Quite a few original elements are included in the author’s approach. This approach is compared to other possibilities of describing dynamics of multi-body systems in relative motion. The author’s method makes use of Kane’s equations that are opposed in the paper to the Newton-Euler approach that is used most often in the analogous applications. Numerical implementation of the theoretical results is also presented and a sample of the corresponding numerical analysis. Both these show the particular way to model dynamics of such systems efficiently and what consequences might be of the simplification in the description of relative motion. This appears to be more important than it is usually believed, particularly when accelerating or breaking the vehicle.

Relative Motion and the Geometry of Formations in Keplerian Elliptic Orbits with Arbitrary Eccentricity

The well-known Hill-Clohessy-Wiltshire equations that are used for the design of formation flight relative orbits are based on a circular reference orbit Classical solutions such as the projected circular or general circular relative orbit are no longer valid in the presence of eccentricity. This paper studies the effects of eccentricity on relative motion for Keplerian orbits. A new linear condition for bounded motion in relative position coordinates is derived that is valid for arbitrary eccentricities and epoch of the reference orbit. It is shown that the solutions to the Tschauner-Hempel equations that are used for rendezvous in elliptic orbits are directly related to the description of relative motion using small orbital element differences. A meaningful geometric parameterization for relative motion near a Keplerian elliptic orbit of arbitrary eccentricity is also developed. The eccentricity-induced effects are studied and exploited to obtain desired shapes of the relative orbit. Equations relating these parameters to initial conditions and differential classical and nonsingular elements are also derived. This parameterization is very useful for the analysis of more complicated models, such as the nonlinear relative motion problem.

Useful relative motion description method for Perturbations analysis in satellite Formation flying

A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying. With the help of these parameters, the effect of the perturbations on the relative orbit trajectory and geometric properties of satellite formation can be easily analyzed. First,the relative orbital elements are derived, and pointed out: if the eccentricity of the leading satellite is a small value, the relative orbit trajectory is determined by the intersection between an elliptic cylinder and a plane in the leading satellite orbit frame reference; and the parameters that describe the elliptic cylinder and the plane can be used to obtain the relative orbit trajectory and the relative orbital elements. Second, by analyzing the effects of gravitational perturbations on the relative orbit using the relative orbital elements,it is found that the propagation of a relative orbit consists of two parts: one is the drift of the elliptic cylinder; and the other is the rotation of the plane resulted from the rotation of the normal of the plane. Meanwhile, the analytic formulae for the drift and rotation rates of a relative trajectory under gravitational perturbations are presented. Finally, the relative orbit trajectory and the corresponding changes were analyzed with respect to the J2 perturbation.

About Rotational Transitions and Muon Transfer in Muonic Hydrogen–Helium Systems

Rotational J=1→J=0 transitions in muonic molecule, (3Heμd)J++, in [(3Heμd)++,2e]–D and [(3Heμd)++,e]+–D collisions are considered. The corresponding cross sections and reaction rates are calculated in the frame of the semi-classical approximation using He–H(H+) and He+–H(H+) interaction potentials. The results obtained are about two orders of magnitudes smaller than the corresponding quantum-mechanical ones calculated previously by the authors using plane-waves for description of relative motion of the subsystems. Reaction rates for radiative and Auger muon transfer from hydrogen to helium are also calculated semi-classically. The corresponding results are close to the quantum-mechanical ones published elsewhere.

Stochastic theory of collisional energy transfer: quantum description of translation in a model problem

Master equation transition probabilities, both quantum and semiclassical, are compared with exact quantum calculations for the Landau-Teller model. The quantum description of relative motion during a collision is found to be important for low relative energies.

Contact localization and motion analysis in the ocean environment: A perspective

This paper presents a perspective on contact localization and motion analysis (CLMA) in the ocean environment. Such well-studied cases as passive hearings-only contact motion analysis, multipath ranging, and localization/tracking via arrays are used to illustrate the concept. The performance of current CLMA systems is shown to depend on the type and characteristics of the basic measurements developed by their time delay estimators, the acoustic channels linking contact and observer, and the type and description of relative motion between contact and observer. General classes of CLMA schemes are presented. Complexity is shown to depend on the linearity/nonlinearity of their solution equations, the degree to which a contact is observable at each sample time, and the relative motion between contact and observer. Contributions to total system gain, biasing issues, and candidate solutions are discussed. Comprehensive references are provided.