Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun,Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition.In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth–Moon system,and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.     

Input shaping control of a nuclear power plant’s fuel transport system

In this paper, the residual vibration control problem of a nuclear power plant’s fuel-transport system is discussed. The purpose of the system is to transport fuel rods to the target position within the minimum time. But according to observations, the rods oscillate at the end of the maneuver, causing an undesirable delay in the operation and affecting the system’s performance in terms both of productivity and of safety. In the present study, a mathematical model of the system was developed to simulate the under-water sway response of the rod while keeping in view the effects of the hydrodynamic forces imposed by the surrounding water. Experiments were performed to validate the model’s correctness. Further, simulation results were used to design the input shaping control that generates shaped velocity commands for transport of the fuel rods to the target position with the minimum residual vibration. It was observed that due to the under-water maneuvering, the fuel-handling system behaves as a highly damped process and that the generated shaped velocity commands fail to effect the desired suppression of the residual vibration. Therefore, keeping in view the highly damped nature of the system, a modified shaped command was generated that transported the fuel rods to the target position with the minimum residual vibration.     

Nonlinear characteristics of a multi-degree-of-freedom wind turbine’s gear transmission system involving friction

Nonlinear Dynamics - In this study, a 42-degree-of-freedom (42-DOF) translation–torsion coupling dynamic model of the wind turbine’s compound gear transmission system considering...     

Exploration of Saint-Venant’s Principle in Inertial High Strain Rate Testing of Materials

Current high strain rate testing procedures of materials are limited by poor instrumentation which leads to the requirement for stringent assumptions to enable data processing and constitutive model identification. This is the case for instance for the well known Split Hopkinson Pressure Bar (SHPB) apparatus which relies on strain gauge measurements away from the deforming sample. This paper is a step forward in the exploration of novel tests based on time and space resolved kinematic measurements obtained through ultra-high speed imaging. The underpinning idea is to use acceleration fields obtained from temporal differentiation of the full-field deformation maps measured through techniques like Digital Image Correlation (DIC) or the grid method. This information is then used for inverse identification with the Virtual fields Method. The feasibility of this new methodology has been verified in the recent past on a few examples. The present paper is a new contribution towards the advancement of this idea. Here, inertial impact tests are considered. They consist of firing a small steel ball impactor at rectangular free standing quasi-isotropic composite specimens. One of the main contributions of the work is to investigate the issue of through-thickness heterogeneity of the kinematic fields through both numerical simulations (3D finite element model) and actual tests. The results show that the parasitic effects arising from non-uniform through-the-thickness loading can successfully be mitigated by the use of longer specimens, making use of Saint-Venant’s principle in dynamics.     

Nonlinear dynamics in the flexible shaft rotating–lifting system of silicon crystal puller using Czochralski method

Silicon crystal puller (SCP) is key equipment in silicon wafer manufacture, which is, in turn, the base material for the most currently used integrated circuit chips. With the development of the techniques, the demand for longer mono-silicon crystal rod with larger diameter is continuously increasing in order to reduce the manufacture time and the price of the wafer. This demand calls for larger SCP with an increasing height, though it causes serious swing phenomenon of the crystal seed. The strong swing of the seed increases the possibility of defects in the mono-silicon rod and the risk of mono-silicon growth failure. The main aim of this paper is to analyze the nonlinear dynamics in flexible shaft rotating–lifting (FSRL) system of the SCP. A mathematical model for the swing motion of the FSRL system is derived. The influence of relevant parameters, such as system damping, excitation amplitude, and rotation speed, on the stability and the responses of the system is analyzed. The stability of the equilibrium, bifurcation, and chaotic motion is demonstrated, which have been observed in practical situations. Melnikov method is used to derive the possible parameter region which leads to chaotic motion. Three routes to chaos are identified in the FSRL system, including period doubling, symmetry-breaking bifurcation, and crisis. The work in this paper analyzes and explains the complex dynamics in FSRL system of the SCP, which will be helpful for the designers in the designing process in order to avoid the swing phenomenon in the SCP.

     

Bifurcation analysis for non-local design of a hybrid observer for the impulsive Goodwin’s oscillator

Nonlinear Dynamics - The impulsive Goodwin’s oscillator is a mathematical model capturing the dynamics arising in a closed-loop system, where a third-order linear time-invariant plant is...     

Development and experimental investigation of a Quadrotor’s robust generalized dynamic inversion control system

Nonlinear Dynamics - The development of a two-loops Quadrotor’s robust generalized dynamic inversion (RGDI)-based control system is presented. The outer (position) loop utilizes PD position...     

Refinement of a global model for the Earth’s gravitational field using airborne gravimetry data

An algorithm for combining airborne gravimetry data with the data supplied by a global model of the Earth’s gravitational field is considered. The global model is specified by a spherical wavelet decomposition. An optimal guaranteed estimation of the wavelet coefficients for the gravitational field is used.     

Paradox of a particle’s trajectory moving on a string

This paper deals with the paradoxical properties of the solution of string vibration under a moving mass. The solutions published to date are not simple enough and cannot be applied to investigations in the entire range of mass speeds, including the overcritical range. We propose a formulation of the problem that allows us to reduce the problem to a second-order matrix differential equation. Its solution is characteristic of all features of the critical, subcritical, and overcritical motion. Results exhibit discontinuity of the mass trajectory at the end support point, which has not been previously reported in the literature. The closed solution in the case of a massless string is analyzed and the discontinuity is proved. Numerical results obtained for an inertial string demonstrate similar features. Small vibrations are analyzed, which is why the effect discussed in the paper is of purely mathematical interest. However, the phenomenon results in complexity in discrete solutions.     

A feedback linearization design for the control of vehicle’s lateral dynamics

In this paper, the feedback linearization scheme is applied to the control of vehicle’s lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in (Liaw, D.C., Chung, W.-C. in 2006 IEEE International Conference on Systems, Man, and Cybernetics, 2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. The vehicle dynamics at the saddle node bifurcation point is derived and then decomposed as an affine nominal model plus the remaining term of the overall system dynamics. Feedback linearization scheme is employed to construct the stabilizing control laws for the nominal model. The stability of the overall vehicle dynamics at the saddle-node bifurcation is then guaranteed by applying Lyapunov stability criteria. Since the remaining term of the vehicle dynamics contains the steering control input, which might change system equilibrium except the designed one. Parametric analysis of system equilibrium for an example vehicle model is also obtained to classify the regime of control gains for potential behavior of vehicle’s dynamical behavior.     

Free energy calculation of single molecular interaction using Jarzynski’s identity method: the case of HIV-1 protease inhibitor system

Jarzynski’ identity(JI) method was suggested a promising tool for reconstructing free energy landscape of biomolecular interactions in numerical simulations and experiments.However,JI method has not yet been well tested in complex systems such as ligand-receptor molecular pairs.In this paper,we applied a huge number of steered molecular dynamics(SMD) simulations to dissociate the protease of human immunodeficiency type I virus(HIV-1 protease) and its inhibitors.We showed that because of intrinsic complexity of the ligand-receptor system,the energy barrier predicted by JI method at high pulling rates is much higher than experimental results.However,with a slower pulling rate and fewer switch times of simulations,the predictions of JI method can approach to the experiments.These results suggested that the JI method is more appropriate for reconstructing free energy landscape using the data taken from experiments,since the pulling rates used in experiments are often much slower than those in SMD simulations.Furthermore,we showed that a higher loading stiffness can produce higher precision of calculation of energy landscape because it yields a lower mean value and narrower bandwidth of work distribution in SMD simulations.     

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev’s type

For a nonholonomic system of Chetaev’s type, the conformal invariance and the conserved quantity of Mei symmetry for Appell equations are investigated. First, under the infinitesimal one-parameter transformations of group and the infinitesimal generator vectors, Mei symmetry and conformal invariance of differential equations of motion for the system are defined, and the determining equation of Mei symmetry and conformal invariance for the system are given. Then, by means of the structure equation to which the gauge function is satisfied, the Mei-conserved quantity corresponding to the system is derived. Finally, an example is given to illustrate the application of the result.