Khaled I. Nawafleh

HAMILTON JACOBI TREATMENT OF CONSTRAINED SYSTEMS

One approach for solving mechanical problems of constrained systems using the Hamilton–Jacobi formulation is examined. The Hamilton–Jacobi function is obtained in the same manner as for regular systems. This is used to determine the solutions of the equations of motion for constrained systems.

Hamilton–Jacobi Treatment of Lagrangians with Linear Velocities

A new approach for solving mechanical problems of Linear Lagrangian systems using the Hamilton–Jacobi formulation is proposed. The equations of motion are recovered from the action integral. It has been proved that there is no need to follow the consistency conditions of the Dirac approach.

CANONICAL QUANTIZATION OF DISSIPATIVE SYSTEMS

Innovation is the application of new knowledge and its materialization. Thus it ensures the companys ability to cope with changes in the business environment and the ability to survive in the global competitive environment. As a result, innovation saves natural resources, provides safe and more efficient transport and production. Innovations change the style of work life, place emphasis on the importance of education, creativity, communication and collaboration. However, innovations are associated with a number of problems. They require high costs of the research and development and they face the risks during implementation. This paper describes specific experience with the application of principles and tools of logistics, project management and mainly the application of management system created for the streamlining not only the process of preparation and implementation of the specific innovation project, but also for the streamlining the operation of research and development workplace which implement innovative projects.

The Motion of a Spinning Particle in an External Electromagnetic Field as a Constrained System

Abstract The motion of a spinning point-particle in an external electromagnetic field is investigated as a constrained system. The comparison with the Dirac equation is discussed, and it is shown that the primary constraint can be derived explicitly from this equation. Further, the equations of motion are determined using the canonical method. The quantization of such a system is achieved using the WKB approximation.

Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian

In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamiltons equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.

Constrained motion of a particle on an elliptical path

Abstract In this work we investigate the constrained motion of a particle on an ellipse in the framework of two approaches: the standard approach and Dirac’s approach. The Poisson brackets and the Dirac brackets of the generalized variables are calculated by using Scardicchio’s technique, and it is observed that there exist nonconserved quantities in the system. On the quantum level, the nonvanishing commutators between the generalized variables lead to the principle of uncertainty. However, in the limit case of motion on a circle the generalized momentum is found to be a constant of motion.

THE HAMILTON–JACOBI ANALYSIS OF OPTICAL WAVEGUIDES

In this paper, the Hamilton–Jacobi method for solving differential equations of wave propagation is investigated. It is shown that when a wave propagates through a background medium that varies slowly on the scale of the wavelength, the trajectory of the light particle follows the usual rule of refraction.