Modified RATTLE Method for Rigid Body Dynamics in Cartesian Coordinates

In this paper,we describe a modified RATTLE(M-RATTLE)method for rigid body dynamics directly in Cartesian coordinates.The M-RATTLE method introduces a new way of resetting the coordinates to satisfy the constraints at each step,which is designed for the rigid body dynamics calculations in the Cartesian coordinates.M-RATTLE is algebraically equivalent to the RATTLE method and the cost of performing rigid body dynamics by M-RATTLE is independent of the number of constraints.The interaction forces between atoms belonging to the same rigid molecule do not need to be computed and explicit expressions of the constraints of internal degrees of freedom are unnecessary.The performance and sampling results of the proposed method are compared with those of the symplectic splitting method for an isolated rigid benz molecule and for a cluster of twenty-seven benz molecules.

On Flexible Trajectory Description for Effective Rigid Body Motion Reproduction and Recognition

Recognizing and reproducing spatiotemporal motions are necessary when analyzing behaviors andmovements during human-robot interaction. Rigid body motion trajectories are proven as compact and informativeclues in characterizing motions. A flexible dual square-root function (DSRF) descriptor for representing rigid bodymotion trajectories, which can offer robustness in the description over raw data, was proposed in our previousstudy. However, this study focuses on exploring the application of the DSRF descriptor for effective backwardmotion reproduction and motion recognition. Specifically, two DSRF-based reproduction methods are initiallyproposed, including the recursive reconstruction and online optimization. New trajectories with novel situationsand contextual information can be reproduced from a single demonstration while preserving the similarities withthe original demonstration. Furthermore, motion recognition based on DSRF descriptor can be achieved byemploying a template matching method. Finally, the experimental results demonstrate the effectiveness of theproposed method for rigid body motion reproduction and recognition.

Periodic Orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies

We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of (h is energy constant;μ is mass ratio of the two primaries;are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.

Sensitivity Analysis of the Effect of Speed and Inclination Angle on Water-Entry Slamming Pressure of the Bow

In this paper,a method about the water-entry slamming of a two-dimensional(2D)bow structure has been proposed based on the experimental and simulation results.According to this method,the sensitivity analysis has been carried out about the effect of speed and inclination angle on the slamming pressure of the bow.Firstly,a 2D ship bow experimental model was performed to obtain the slamming pressure distribution at different measuring points under different speeds.Then,numerical simulation for the water-entry slamming of this experimental model was conducted to obtain the pressure distribution on the experimental model under different working conditions.Finally,the experimental results were compared with the numerical simulation results to evaluate the effect of speed and inclination angle on the slamming pressure of the bow.The results show that the slamming pressure is more sensitive to speed variation within the low-speed range.The effect of inclination angle on the slamming pressure is more obvious in the small angle condition.When the inclination angle is larger than 45°,the effect is limited.

Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics

In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.

THE INVARIANT MANIFOLD METHOD AND THE CONTROLLABILITY OF NONLINEAR CONTROL SYSTEM

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A.M.Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results. Based on Kovalev’s oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition was discussed. At last, the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.

Simulation of Water-Soil-Structure Interactions Using Incompressible Smoothed Particle Hydrodynamics

In the present work,an incompressible smoothed particle hydrodynamic(SPH)method is introduced to simulate water-soil-structure interactions.In the current calculation,the water is modelled as a Newtonian fluid.The soil is modelled in two different cases.In the first case,the granular material is considered as a fluid where a Bingham type constitutive model is proposed based on Mohr-Coulomb yield-stress criterion,and the viscosity is derived from the cohesion and friction angle.In addition,the fictitious suspension layers between water and soil depending on the concentration of soil are introduced.In the second case,Hooke’s law introduces elastic soil.In ISPH,the pressure is evaluated by solving the pressure Poisson equation using a semi-implicit algorithm based on the projection method and an eddy viscosity for water is modelled by a large eddy simulation with the Smagorinsky model.In the proposed ISPH method,the pressure is stabilized to simulate the multiphase flow between soil and water.Numerical experiments for water-soil suspension flow of Louvain erosional dam break with flat soil foundation,is simulated and validated using 3D-ISPH method.Coupling between water-soil interactions with different solid structures are simulated.The results revealed that,the suspension layers with the Bingham model of soil gives more accurate results in the experiment as compared to the case of the Bingham model without suspension layers.In addition,the elastic soil model by the Hooke’s law can simulate soil hump accurately as compared to the Bingham model.From the simulations,avoiding erosion behind the structure for preventing the structure break during flood are investigated by using an extended structure or a wedge structure.

A Method of Disc Inclination Correction Based on the Inversion Model of Rotation Law

Under the traditional dynamic model,the conventional method for solving the rotation angle of a rigid body is to use the fixed-axis rotation law of the rigid body,but the known rotation shaft position must be used as a prerequisite.In practical work,for the rotation of a rigid body under multiple forces,solving the shaft is often a difficult problem.In this paper,we consider the rigid body of the disc is subjected to the force of uneven magnitude from multiple angles,the position of the rotating shaft is obtained by iterative inversion through the rigid body rotation law and the dichotomy method.After the position of the shaft is determined,we establish a differential equation model based on the law of rigid body rotation,the rotation angle of the rigid body thus being solved based on this model.Furthermore,an optimization algorithm such as genetic algorithm is used to search for a correction scheme to return the rigid body to equilibrium at any given deflection angle.The model and method are based on computer to explore the law of rotation,the practical application of them play an important role in studying the concentric drum movement and the balance of handling furniture.

Bionic Attitude Transformation Combined with Closed Motion for a Free Floating Space Robot

In order to realize the small error attitude transformation of a free floating space robot,a new method of three degrees of freedom( DOF) attitude transformation was proposed for the space robot using a bionic joint. A general kinematic model of the space robot was established based on the law of linear and angular momentum conservation. A combinational joint model was established combined with bionic joint and closed motion. The attitude transformation of planar,two DOF and three DOF is analyzed and simulated by the model,and it is verified that the feasibility of attitude transformation in three DOF space. Finally,the specific scheme of disturbance elimination in attitude transformation is presented and simulation results are obtained.Therefore,the range of application field of the bionic joint model has been expanded.

Investigation of power-type variational principles in liquid-filled system

Starting from the basic equations of hydrodynamics, the maximum powertype variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic-liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liquid coupling dynamics can be easily numerically modeled.Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures.

Power and Damping Torque of Electric-Quadrupole Radiation for Rotational Charged Rigid Bodies

Based on the basic theory of electrodynamics about electromagnetic radiation,the general formulae of radiation power and damping torque of electric-quadrupole moment for a steadily and uniformly charged rigid body with any periodic rotation are derived.The concise form of the formulae in some special symmetric cases are deduced and discussed,and the results of several common symmetric charged bodies are listed.

Relationship between contact size and static friction:An approach for rigid crystalline surfaces

Relationship between contact size(A)and static friction(f)has been studied for rigid crystalline systems.We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction.In these systems,there are numerous nontrivial commensurate contacts.Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact.For commensurate contacts,f∝A independent of the shape.For incommensurate contacts,generally f∝A^(0) for regular shapes or f∝A^(1/4) for irregular shapes;however,in very few cases of regular shapes,f∝A^(1/2).Moreover,in above systems,commensurability of a contact can be easily changed by a perturbation of the misfit angle.Therefore,if the perturbation caused by the lateral force and the deformation of the surface are considered(as is the case in real systems),further research is necessary.

Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies

In this paper we present how nonlinear stochastic Itˆo differential equations arising in the modelling of perturbed rigid bodies can be solved numerically in such a way that the solution evolves on the correct manifold.To this end,we formulate an approach based on Runge-Kutta–Munthe-Kaas(RKMK)schemes for ordinary differ-ential equations on manifolds.Moreover,we provide a proof of the mean-square convergence of this stochastic version of the RKMK schemes applied to the rigid body problem and illustrate the effectiveness of our proposed schemes by demonstrating the structure preservation of the stochastic RKMK schemes in contrast to the stochastic Runge-Kutta methods.

Current state and progress of research on forensic biomechanics in China

Forensic biomechanics gradually has become a significant component of forensic science.Forensic biomechanics is evidence-based science that applies biomechanical principles and methods to forensic practice,which has constituted one of the most potential research areas.in this review,we introduce how finite element techniques can be used to simulate forensic cases,how injury criteria and injury scales can be used to describe injury severity,and how tests of postmortem human subjects and dummy can be used to provide essential validation data.This review also describes research progress and new applications of forensic biomechanics in China.

DESIGN AND IMPLEMENTATION OF REAL-TIME PHYSICS SIMULATION ENGINE FOR e-ENTERTAINMENT

We present our recent research results regarding the designing and implementation of real-time physics simulation engines,which aim at developing physics-inspired e-entertainment such as computer games,mobile applications,interactive TV and other smart media in Korea.Our real-time physics engine consists of three functional components:rigid body dynamics simulation,deformable body simulation,and data-driven physics simulation.The core simulation techniques to realize these simulation components include real-time collision detection and response,large-scale model simulation,and character model control.In this paper,we highlight these features and demonstrate their performances.We also showcase some of the gaming applications that we have integrated our physics engine into.