Papers by Keyword: Lagrangian

Abstract: In this paper, starting from recent data provided by the National Institute of Statistics, we analyze the tourism activity in Mehedinți County. We apply the regression method and analyze some models. We also compare the economic results with those of previous years. Also, in this paper we study the stability of dynamic systems with applications in economics. The stability study is done using the Leapunov function method. The originality of the paper consists in the way we choose the mathematical model in case of regression and in the way we choose the Leapunov function in case of dynamic systems in which we analyze stability.

Abstract: The paper includes the stability study of some dynamical systems given by systems of differential equations. The paper examines the stability of three dynamic systems using the Leapunov function method. The originality of the paper consists of how we choose the Leapunov function. We apply the stability theorems given by Leapunov for autonomous systems. Stability is an important property of a dynamic system that has applications in the technique.

Abstract: Aiming at the attitude interference of space mechanical arm of free-flying space robot (FFSR) against the satellite body, parallel coordination motion control technology for space mechanical arm and satellite body is proposed in this paper. Firstly, the position and velocity at any point based on FFSR system can be expressed as a set of functions consisting of chain pole centroid vectors, and the kinematic model for FFSR has been set up. Secondly, the compact form of dynamical model in system centroid vector function for FFSR is set up with Lagrange method. Finally, inherent redundancy characteristic of FFSR system is applied to propose the parallel coordination motion control technology which simultaneously and effectively controls the motions of F satellite body and configuration of space mechanical arm. Transposition Jacobi controller with inertia feedback has been developed.

Abstract: The foundations of micro-milling are similar to macro-milling but the phenomena it involves are not a simple scaling-down of macro-cutting. The importance of the minimum chip thickness is one of the significant differences between the two processes. The lagrangian FEM model presented in this paper aims to study the depth of cut influence on chip formation of Ti6Al4V in orthogonal cutting. It is firstly used to compare the modelled saw-toothed macro-chip morphology and cutting forces to experimental cutting results from literature. Then a minimum chip thickness prediction is performed by decreasing the depth of cut. Finally this study is the opportunity to highlight the specific features of micro-cutting reported in literature, such as the effective negative rake angle of the tool or the size effect. The model presented brings therefore a numerical contribution to the comprehension of these phenomena.

Abstract: Investigation of the properties of peptide plane in protein chain from both classical and quantum approach is presented. We calculated interatomic force constants for peptide plane and hydrogen bonds between peptide planes in protein chain. On the basis of force constants, displacements of each atom in peptide plane, and time of action we found that the value of the peptide plane action is close to the Planck constant. This indicates that peptide plane from the energy viewpoint possesses synergetic classical/quantum properties. Consideration of peptide planes in protein chain from information viewpoint also shows that protein chain possesses classical and quantum properties. So, it appears that protein chain behaves as a triple dual system: (1) structural - amino acids and peptide planes, (2) energy - classical and quantum state, and (3) information - classical and quantum coding. Based on experimental facts of protein chain, we proposed from the structure-energy-information viewpoint its synergetic code system.