DISCUSSION OF THE CENTER OF MASS MOTION IN A SYSTEM WITH THREE DEGREES OF FREEDOM

2013 ◽  
Vol 22 (06) ◽  
pp. 1350043
Author(s):  
WERNER SCHEID
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Hermite Polynomials ◽  
Wave Functions ◽  
Basis Set ◽  
Mass Motion ◽  
Laboratory System ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Three Degrees Of Freedom

This paper considers the problem of the center of mass motion of three fermionic particles, e. g., equal nucleons (no spin), which can move only in the x-direction in the laboratory system. This system (with three degrees of freedom only) is transformed to a system where one coordinate is proportional to the center of mass coordinate. The center of mass moves in a harmonic oscillator potential. The basis set of wave functions is constructed with Hermite polynomials in part. As example we study the case of a quadratic intrinsic potential between the particles. The problem may be important for the motion of three nucleons in a crystal channel.

ATOMIC VELOCITY SELECTION BY INTERFERENCE IN TWO-PHOTON IONIZATION

1996 ◽  
Vol 05 (04) ◽  
pp. 911-919
Author(s):  
J.C. GARREAU ◽  
D. WILKOWSKI ◽  
D. HENNEQUIN ◽  
V. ZEHNLÉ
Keyword(s):  
Electromagnetic Field ◽  
Quantum Interference ◽  
Quantum Coherence ◽  
Degrees Of Freedom ◽  
Internal State ◽  
Center Of Mass ◽  
Mass Motion ◽  
Two Photon ◽  
Selective Ionization ◽  
Velocity Selection

This paper discusses a new scheme for generating quantum coherence between different degrees of freedom of an atom interacting with two modes of the electromagnetic field. The presence of quantum interference in a two-photon coupling between the ground state of the atom and the continuum through two quasi-resonant intermediate states induces selective ionization of the atoms for particular combinations of the different parameters characterizing the degrees of freedom of the system, leading to quantum coherence between the internal state, the center-of-mass motion of the atom, and the electromagnetic field. The application of this method to the selection of an atomic velocity class is discussed.

Vehicle Dynamics Model Establishing and Dynamic Characteristic Simulation

2013 ◽  
Vol 404 ◽  
pp. 244-249
Author(s):  
Rui Wang ◽  
Hao Zhang ◽  
Xian Sheng Li ◽  
Xue Lian Zheng ◽  
Yuan Yuan Ren
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Rear Wheel ◽  
Front Wheel ◽  
Step Response ◽  
Steering Wheel ◽  
Vehicle Simulation ◽  
Equivalent Mechanical Model ◽  
External Forces ◽  
Three Degrees Of Freedom

By establishing bus simplify coordinate system model and equivalent mechanical model, inertial forces and external forces are analyzed through vehicle lateral movement and vehicle's yaw motion and roll motion. Three degrees of freedom linear motion equation of vehicle is established taking into account lateral motion, yawing movement and rolling motion of vehicle and it can be solved by using method of state space equation. Vehicle dynamic characteristics are analyzed by using this method and programming with Matlab. Vehicle in steering wheel angle step response is analyzed under the conditions of different tire wheel cornering stiffness, moment of inertia, height of center of mass. The results show that increasing rear wheel cornering stiffness, reducing front wheel cornering stiffness and center of mass height, which can effectively improve stability of vehicle. Simulation results provide a theoretical basis and reference for the selection and design of vehicle.

scholarly journals Charge density distributions for odd-A of 2s-1d shell nuclei

2010 ◽  
Vol 7 (2) ◽  
pp. 1028-1033
Author(s):  
Baghdad Science Journal
Keyword(s):  
Charge Density ◽  
Wave Functions ◽  
Mean Square ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Charge Radii ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The Difference ◽  
Remarkable Agreement

An analytical expression for the charge density distributions is derived based on the use of occupation numbers of the states and the single particle wave functions of the harmonic oscillator potential with size parameters chosen to reproduce the observed root mean square charge radii for all considered nuclei. The derived expression, which is applicable throughout the whole region of shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- of shell nuclei, such as and nuclei. It is found that introducing an additional parameters, namely and which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkable agreement between the calculated and experimental results of the charge density distributions throughout the whole range of

scholarly journals ON AN EXPLICIT SET OF COMPLETE EIGENFUNCTIONS FOR THE CALOGERO–SUTHERLAND MODEL

1996 ◽  
Vol 11 (11) ◽  
pp. 891-898 ◽  
Author(s):  
N. GURAPPA ◽  
PRASANTA K. PANIGRAHI
Keyword(s):  
Center Of Mass ◽  
Operator Method ◽  
Basis Set ◽  
Mass Motion ◽  
Sutherland Model

An operator method is provided to generate an explicit set of complete eigenfunctions for the Calogero–Sutherland model, obtained earlier by Vacek, Okiji and Kawakami, through a special ansatz. We find the connection of the above basis set with the general eigenfunctions of this model and explicitly show that these states describe only the center-of-mass motion.

Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations

1958 ◽  
Vol 245 (1240) ◽  
pp. 128-145 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Wave Functions ◽  
Coupling Scheme ◽  
Nuclear Shell Model ◽  
Model Framework ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Classification Schemes ◽  
Nuclear Shell

To understand how collective motion can develop in the shell-model framework it is necessary to study configuration interaction. With this in mind, group-theoretical methods are used to investigate the possible classification schemes for a number of nucleons in m xed configurations. One particular coupling scheme, which is associated with the degeneracy of a harmonic oscillator potential and which, in a following paper, will be shown to have collective properties is described in detail. The wave functions in this scheme are seen to be very similar to those resulting from an actual shell-model calculation with configurational mixing.

Energy-Based Attitude Control of Spherical Pendulum

2011 ◽  
Vol 143-144 ◽  
pp. 355-359
Author(s):  
Wen Jun Lv ◽  
Xin Sheng Ge
Keyword(s):  
Rigid Body ◽  
Attitude Control ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Center Of Mass ◽  
Control Law ◽  
Spherical Pendulum ◽  
Axis Of Symmetry ◽  
Passive Theory ◽  
Three Degrees Of Freedom

In this paper, we study the attitude control problems based on model of spherical pendulum. Three degrees of freedom pendulum (3D pendulum) is a rigid body supported by a frictionless pivot. According to relative position of the center of mass and the fixed pivot without friction, the 3D rigid pendulum can be divided into two balanced attitudes, Hanging equilibrium and inverted equilibrium. For the axisymmetric 3D rigid pendulum, the axis of symmetry is equivalent to axis of inertia of rigid body, and angular velocity around the axis of symmetry is equal to zero, as a result, the 3D rigid pendulum can be equal to the spherical pendulum. According to the motion attitude of spherical pendulum, one control method based on passive theory is proposed in this paper, Firstly, we use the passive theory to research the equilibrium stability of spherical pendulum. Secondly, passive theory and the Lyapunov function are utilized to deduce the control law .Finally, the spherical pendulum reach asymptotically stable in equilibrium position.

q-DEFORMED ALGEBRAS AND THE TWO-ANYON PROBLEM

1996 ◽  
Vol 11 (18) ◽  
pp. 1489-1495 ◽  
Author(s):  
P. ROY
Keyword(s):  
Magnetic Field ◽  
Harmonic Oscillator ◽  
Constant Magnetic Field ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Deformed Algebras ◽  
Symmetry Algebras

It is shown that the two-anyon system in a harmonic oscillator potential and in a constant magnetic field admits certain q-deformed symmetry algebras realized over the space of wave functions of the respective systems.

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