Velocity pointing error reduction for symmetric spinning spacecraft via a two-burn scheme

2019 ◽  
Vol 41 (14) ◽  
pp. 3877-3886
Author(s):  
Zhenhua Liang ◽  
Wenhe Liao ◽  
Xiang Zhang
Keyword(s):  
Angular Velocity ◽  
Initial Conditions ◽  
Center Of Mass ◽  
Euler Angle ◽  
Error Reduction ◽  
Constant Mass ◽  
Pointing Error ◽  
Lower Spin ◽  
New Form ◽  
Minimum Velocity

During axial thrusting of a symmetric spinning spacecraft, misalignment and center-of-mass offset can cause unwanted body-fixed torques. The two-burn scheme is applied to eliminate velocity pointing error. Solutions for angular velocity, Euler angle, and inertial velocity with nonzero initial conditions are derived in a new form for axisymmetric spacecraft with constant mass. Simulations show that the solutions closely match numerical simulations and the two-burn scheme decrease the velocity pointing error obviously. Based on the solutions, the effect of two-burn scheme is analyzed. The results show that the spacecraft will obtain the minimum velocity pointing error if the burn and coast times are controlled accurately. Also, the two-burn scheme allows for a lower spin rate and the spacecraft can be maneuvered at nonzero initial conditions compared with the continuous thrust scheme.

Kinematic characteristics of longitudinal double folding wings

2021 ◽  
pp. 1-25
Author(s):  
L. Tiegang ◽  
C. Guoguang ◽  
L. Shuai
Keyword(s):  
Angular Velocity ◽  
Structural Model ◽  
Initial Conditions ◽  
Aerodynamic Force ◽  
Model Simulation ◽  
Lagrange Equation ◽  
Grid Method ◽  
Weapon Systems ◽  
Folding Wing ◽  
Double Folding

ABSTRACT A folding wing is a tactical missile launching device that needs to be miniaturised to facilitate storage, transportation, and launching; save missile and transportation space; and improve the combat capability of weapon systems. This study investigates the aeroelastic characteristics of the secondary longitudinal folding wing during the unfolding process. First, the Lagrange equation is used to establish the structural dynamics model of the folding wing, the kinematics characteristics during the deformation process are analysed, and the unfolding movement of the folding wing is obtained using the dynamic equations in the process. Then, the generalised unsteady aerodynamic force is calculated using the dipole grid method, and the multi-body dynamics equation of the folding wing is obtained. The initial angular velocity required for the deployment of the folding wing is analysed through structural model simulation, and the influence of the initial angular velocity on the opening process is studied. Finally, aeroelastic flutter analysis is performed on the folding wing, and the physical model of the folding wing verified experimentally. Results show that the type of aeroelastic response is sensitive to the initial conditions and the way the folding wing opens.

scholarly journals Dynamics of Space Particles and Spacecrafts Passing by the Atmosphere of the Earth

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vivian Martins Gomes ◽  
Antonio Fernando Bertachini de Almeida Prado ◽  
Justyna Golebiewska
Keyword(s):  
Initial Conditions ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
The Sun ◽  
Three Body Problem ◽  
The Earth ◽  
Before And After ◽  
Three Body ◽  
Body Energy ◽  
Spacecraft Position

The present research studies the motion of a particle or a spacecraft that comes from an orbit around the Sun, which can be elliptic or hyperbolic, and that makes a passage close enough to the Earth such that it crosses its atmosphere. The idea is to measure the Sun-particle two-body energy before and after this passage in order to verify its variation as a function of the periapsis distance, angle of approach, and velocity at the periapsis of the particle. The full system is formed by the Sun, the Earth, and the particle or the spacecraft. The Sun and the Earth are in circular orbits around their center of mass and the motion is planar for all the bodies involved. The equations of motion consider the restricted circular planar three-body problem with the addition of the atmospheric drag. The initial conditions of the particle or spacecraft (position and velocity) are given at the periapsis of its trajectory around the Earth.

The Road to Chaos by Time-Asymmetric Hebbian Learning in Recurrent Neural Networks

2007 ◽  
Vol 19 (1) ◽  
pp. 80-110 ◽  
Author(s):  
Colin Molter ◽  
Utku Salihoglu ◽  
Hugues Bersini
Keyword(s):  
Supervised Learning ◽  
Hebbian Learning ◽  
Learning Algorithm ◽  
Initial Conditions ◽  
A Priori ◽  
Computational Cost ◽  
Chaotic Regime ◽  
Dynamical Regime ◽  
New Form ◽  
The Impact

This letter aims at studying the impact of iterative Hebbian learning algorithms on the recurrent neural network's underlying dynamics. First, an iterative supervised learning algorithm is discussed. An essential improvement of this algorithm consists of indexing the attractor information items by means of external stimuli rather than by using only initial conditions, as Hopfield originally proposed. Modifying the stimuli mainly results in a change of the entire internal dynamics, leading to an enlargement of the set of attractors and potential memory bags. The impact of the learning on the network's dynamics is the following: the more information to be stored as limit cycle attractors of the neural network, the more chaos prevails as the background dynamical regime of the network. In fact, the background chaos spreads widely and adopts a very unstructured shape similar to white noise. Next, we introduce a new form of supervised learning that is more plausible from a biological point of view: the network has to learn to react to an external stimulus by cycling through a sequence that is no longer specified a priori. Based on its spontaneous dynamics, the network decides “on its own” the dynamical patterns to be associated with the stimuli. Compared with classical supervised learning, huge enhancements in storing capacity and computational cost have been observed. Moreover, this new form of supervised learning, by being more “respectful” of the network intrinsic dynamics, maintains much more structure in the obtained chaos. It is still possible to observe the traces of the learned attractors in the chaotic regime. This complex but still very informative regime is referred to as “frustrated chaos.”

CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA

2000 ◽  
Vol 10 (05) ◽  
pp. 997-1018 ◽  
Author(s):  
M. IÑARREA ◽  
V. LANCHARES
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Center Of Mass ◽  
Melnikov Method ◽  
Moments Of Inertia ◽  
Suitable Parameter ◽  
Nutation Angle ◽  
Principal Axes ◽  
Reorientation Process ◽  
Subharmonic Resonances

We study the spin-up dynamics of a dual-spin spacecraft containing one axisymmetric rotor which is parallel to one of the principal axes of the spacecraft. It will be supposed that one of the moments of inertia of the platform is a periodic function of time and that the center of mass of the spacecraft is not modified. Under these assumptions, it is shown that in the absence of external torques and spinning rotors the system possesses chaotic behavior in the sense that it exhibits Smale's horseshoes. We prove this statement by means of the Melnikov method. The presence of chaotic behavior results in a random spin-up operation. This randomness is visualized by means of maps of the initial conditions with final nutation angle close to zero. This phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the presence of subharmonic resonances.

scholarly journals Decentralized Bioinspired Non-Discrete Model for Autonomous Swarm Aggregation Dynamics

2020 ◽  
Vol 10 (3) ◽  
pp. 1067
Author(s):  
Panagiotis Oikonomou ◽  
Stylianos Pappas
Keyword(s):  
Learning Strategy ◽  
Polynomial Regression ◽  
Initial Conditions ◽  
Cost Minimization ◽  
Center Of Mass ◽  
Scalar Fields ◽  
Discrete State ◽  
Robotic Swarms ◽  
Discrete Mathematical Model ◽  
Basin Hopping

In this paper a microscopic, non-discrete, mathematical model based on stigmergy for predicting the nodal aggregation dynamics of decentralized, autonomous robotic swarms is proposed. The model departs from conventional applications of stigmergy in bioinspired path-finding optimization, serving as a dynamic aggregation algorithm for nodes with limited or no ability to perform discrete logical operations, aiding in agent miniaturization. Time-continuous simulations were developed and carried out where nodal aggregation efficiency was evaluated using the following metrics: time to aggregation equilibrium, agent spatial distribution within aggregate (including average inter-nodal distance, center of mass of aggregate deviation from target), and deviation from target agent number. The system was optimized using cost minimization of the above factors through generating a random set of cost datapoints with varying initial conditions (number of aggregates, agents, field dimensions, and other specific agent parameters) where the best-fit scalar field was obtained using a random forest ensemble learning strategy and polynomial regression. The scalar cost field global minimum was obtained through basin-hopping with L-BFGS-B local minimization on the scalar fields obtained through both methods. The proposed optimized model describes the physical properties that non-digital agents must possess so that the proposed aggregation behavior emerges, in order to avoid discrete state algorithms aiming towards developing agents independent of digital components aiding to their miniaturization.

scholarly journals Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Small Parameter ◽  
Initial Conditions ◽  
Geometric Interpretation ◽  
Rigid Bodies ◽  
Parameter Method ◽  
Large Parameter ◽  
Small Parameter Method ◽  
Rotational Motions ◽  
The Stability

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.

scholarly journals Kinematic Pattern of the Drag-Flick: a Case Study

2012 ◽  
Vol 35 (1) ◽  
pp. 27-33 ◽  
Author(s):  
María Gómez ◽  
Cristina López De Subijana ◽  
Raquel Antonio ◽  
Enrique Navarro
Keyword(s):  
Individual Differences ◽  
Angular Velocity ◽  
Relevant Information ◽  
The Other ◽  
Field Hockey ◽  
Optoelectronic System ◽  
Kinematic Pattern ◽  
The Individual ◽  
Minimum Velocity

The drag-flick is more efficient than hits or pushes when a penalty corner situation is in effect in field hockey. Previous research has studied the biomechanical pattern of the drag-flick, trying to find the cues for an optimal performance. On the other hand, some other studies have examined the most effective visual pick-up of relevant information in shots and goalkeeper anticipation. The aim of this study was to analyse the individual differences in the drag-flick pattern in order to provide relevant information for goalkeepers. One female skilled drag-flicker participated in the study. A VICON optoelectronic system (Oxford Metrics, Oxford, UK) was used to capture the drag-flicks with six cameras. The results showed that the main significant differences between right and left shots (p<0.05) in the stick angles, stick minimum angular velocity and front foot-ball distance were when the front foot heel contacted the floor (T1) and at the minimum velocity of the stick, before the dragging action (T3). The findings showed that the most relevant information might be picked up at the ball-and-stick location before the dragging action.

Dynamic bifurcations in non-stationary systems: transitions with an unpredictable outcome

1995 ◽  
Vol 451 (1942) ◽  
pp. 471-485 ◽  
Keyword(s):  
Critical Parameter ◽  
Initial Conditions ◽  
Basins Of Attraction ◽  
Important Concept ◽  
New Form ◽  
Parameter Values ◽  
Dynamic Bifurcations

In nonlinear non-stationary systems, dynamic bifurcations result in a transition to a qualitatively new state. In this paper we examine how the dynamics of transition of such systems may be assessed using the concept of transient basins of attraction. We delineate the phenomenon of indeterminate dynamic bifurcations, where it is shown that the response, after the system passes through critical parameter values, may be extremely sensitive to the choice of initial conditions or parameter states. This new form of unpredictability in systems whose parameters vary with time, is clearly an important concept to be assimilated in the theory of non-stationary dynamics.

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