Relative Dynamics Equations Research Articles

Bubble dynamics equations in Newton fluid

For the high-speed flow of Newton fluid, bubble is produced and expanded when it moves toward the surface of fluid. Bubble dynamics is a very important research field to understand the intrinsic feature of bubble production and motion. This research formulates the bubble expansion by expansion-local rotation transformation, which can be calculated by the measured velocity field. Then, the related dynamic equations are established to describe the interaction between the fluid and the bubble. The research shows that the bubble production condition can be expressed by critical vortex value and fluid pressure; and the bubble expansion rate can be obtained by solving the non-linear dynamic equation of bubble motion. The results may help the related research as it shows a special kind of fluid motion in theoretic sense. As an application example, the nanofiber radium-voltage relation and threshold voltage-surface tension relation in electrospinning process are discussed.

Orbit and attitude control of spacecraft formation flying

Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The present paper focuses on the problem that how to control a chaser satellite to fly around an out-of-work target satellite closely in earth orbit and to track a specific surface. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, considering the uncertainty of inertia, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.

OPTIMAL TRAJECTORY PLANNING OF FORMATION FLYING SPACECRAFT

This paper introduces a closed-loop Guidance and Control optimal algorithm that balances the propellant consumption and the need for collision avoidance among formation flying spacecraft. This model-based algorithm is purely algebraic and computes the spacecraft trajectories from the knowledge of the formation linearized relative dynamics equations and the formation full state. Using Pontryagin's maximum principle, Guidance generates the control inputs required to obtain the optimal trajectory from the current state until the target state, and does so for each of a set of regularly spaced time instants. After each recomputation, Control applies the optimal inputs until the next regularly spaced time instant, when Guidance updates the optimal trajectory again. Simulation results for the algorithm applied to a 3-spacecraft formation in GTO are presented.

An integral solution for the relative-rotation dynamic equation of a cylinder

For the relative rotation dynamic equation of the cylinder between random twain cross sections, we gain an analytic solution for the equation by using the coupling method. Due to the particularity of the equation, we gain an invertible matrix by utilizing the Jordan canonical. Thereby, we obtain an integral solution for the relative rotation dynamic equation of the cylinder. According to the reguirements in engineering applications, we give some analytic solutions of two types of load action, i.e.the impact and periodic types.

Design and Analysis of Suspension Systems with Balanced-Perpendicularly-Guided Structures.

This paper presents the applications of a new vibration wave suppression structure, the balanced-perpendicularly-guided structure (BPGS), to suspension system design. This structure can transfer vibration input into several branches of vibration waves in the perpendicular directions, in a way that the forces of those perpendicularly guided vibration waves are balanced with each other. The radial type, the ring type, and the multiple-ring BPGS suspension systems are introduced. The related dynamic equations are derived, and the frequency response and the transient response are conducted. The perpendicular branches of the BPGS can absorb a large portion of the vibration waves and diminish them by the internal friction. The multiple-ring BPGS system can provide more flexibility in frequency range selection for emphasis to further improve performance.

Towards Fully Probabilistic Control Design

Control design for stochastic systems is traditionally based on the optimization of the expected value of a suitably chosen loss function. This well elaborated and understood task is practically restricted by the computational complexity of the related dynamic programming equations or its equivalents. For this reason, it is worthwhile to search for an alternative formulation which would lead to a more tractable design. Here, such an alternative is presented which leads to a simpler form of design equations. A way is open to a systematic approximation of the optimizing control design. The controller is designed in such a way that Kullback-Leibler distance between probabilistic description of the closed loop and the required description is minimized. It leads to explicit form of a randomized optimal controller which depends on a solution of a functional equation with a simpler structure than general dynamic programming equations. The basic paradigm is proposed and the resulting algorithm is discussed. For illustration purposes, it is applied to linear Gaussian systems. The desirable result is obtained: the optimal controller is determined by a discrete time Riccati equation. Less trivial applications will be treated elsewhere.

Analysis of the temperature rise in the projectile and extended chain polyethylene fiber composite armor during ballistic impact and penetration

AbstractThe ultra‐high strength/modulus, extended chain polyethylene fiber (Spectra® fiber) composite has shown great potential as a lightweight armor material with its extraordinary capability of absorbing the kinetic energy of projectiles. But the relatively low melting point of this fiber (∼ 145°C) has caused concerns regarding the effect of temperature rise during the impact/penetration process on the performance as armor material. In this article, an analysis of temperature rise in projectile and the fiber composite during the impact/penetration process is described. Combining the simulation of impact deformation by finite element analysis and the simulation of temperature rise by a finite difference approximation of the related dynamic equations, the temperature rise caused by the projectile/composite interaction was estimated. Results show that there is a significant temperature rise at the projectile/composite interface due to the friction but that the short length of time involved in the process and the low thermal conductivity of Spectra fiber composite keep the temperature rise in a very small region (in the order of 0.001 cm) around the interface during the impact/penetration process. Consequently, the volume that is affected by the temperature rise is very small, in the order of total 0.001 cm3 around the projectile, and this is too small to generate any detectable effect on the armor performance. After the projectile is stopped, however, substantial heating of fiber composite can occur under specific conditions as the result of heat flow from the hot projectile embedded in the composite. This heating of fibers, however, is a postmortem effect and hence inconsequential to the ballistic performance of the composite armor.