Abstract:
Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of a dynamical system of relative motion are studied. The perturbation to symmetries for the dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Abstract:
This paper studies the Lagrange symmetry of a dynamical system of relative motion. The definition and the criterion of the symmetry of the system are established. The condition under which there exists a conserved quantity and the form of the conserved quantity are obtained.

Abstract:
The optimal velocity model of traffic is extended by taking into account the relative velocity. We derive the stability condition and stimulate the evolution of traffic flow with a small perturbation.We have found that the relative velocity can stabilize traffic flow and decrease the number of jamming phases.

Abstract:
Mei symmetry and Mei conserved quantity deduced directly from Mei symmetry for Appell equations in a dynamical system of the relative motion are investigated. The definition and the criterion of Mei symmetry of Appell equations in a dynamical system of the relative motion under the infinitesimal transformations of groups are given. The expressions of the determining equation of Mei symmetry of Appell equations and Mei conserved quantity deduced directly from Mei symmetry in a dynamical system of the relative motion are gained. An example is given to illustrate the application of the results.

Abstract:
Lie symmetry and Hojman conserved quantity for Nielsen equations in a dynamical system of the relative motion are investigated. The definition and the criterion of Lie symmetry of Nielsen equations in a dynamical system of the relative motion under the infinitesimal transformations of groups are given. The expressions of the determining equation of Lie symmetry of Nielsen equations and Hojman conserved quantity deduced directly from Lie symmetry in a dynamical system of the relative motion are obtained. An example is given to illustrate the application of the results.

Abstract:
In this paper,the formation control and obstacle avoidance problems are dealt with a unified control algorithm,which allows the follower to avoid obstacle while maintaining desired relative bearing or relative distance from the leader.In the known leader-follower robot formation control literature,absolute motion states of the leader robot are required to control the followers, which may not be available in some environments.In this research,the leader-follower robot formation is modelled and controlled in terms of the relative motion states between the leader and follower robots.The absolute motion states of the leader robot are not required in the proposed formation controller.Furthermore,the research has been extended to a novel obstacle avoidance scheme based on sensing the relative motion between robot and obstacle.Experimental investigation has been conducted using the platform consisted of three nonholonomic mobile robots and computer vision system,and the results have demonstrated the effectiveness of the proposed methods.

Abstract:
On the basis of the data of Fujian GPS stations, TAIW and TWTF key observation stations during 1995 to 2003,the variations and relative variations of the lengths between Fujian GPS stations and TAIW and TWTF stations are calculated, in the meantime,strain tensors of TAIW and TWTF stations are also calculated with genetic algorithm. The results show that the crustal relative movement of Taiwan strait is in the tensile state during both the periods of 1995 to 1997 and 2001 to 2003, but the magnitude and the direction of principal strain in the two periods are with a wide variation that may reflect the process of strain energy from accumulation to release before and after the M7.6 Chi-Chi earthquake in 1999.

Abstract:
In this paper, the general expressions of three-order Lagrangian equations in a motional coordinate system are obtained. In coordinate systems with some specific forms of motion, the expressions corresponding to these equations are also presented.