The Rate of Change of an Energy Functional for Axially Moving Continua
| Authors: | Yang Kyung-Jinn, University of Electro-Communications, Japan
Hong Keum-Shik, Pusan National University, Korea, Republic of
Matsuno Fumitoshi, University of Electro-Communications, Japan |
|---|
| Topic: | 2.1 Control Design |
|---|
| Session: | Control of Mechanical and Flexible Systems |
|---|
| Keywords: | Axially moving continua, Leibniz’s rule, transport theorem, Hamilton’s principle, Eulerian and Lagrangian descriptions. |
|---|
Abstract
In this paper, with the utilization of a transport theorem and three-dimensional version of Leibniz’s rule, the procedure for deriving the time rate of change of an energy functional for axially moving continua is investigated. In the control engineering, the correct solution of the time derivation of an energy functional is essential for designing an effective controller, especially, in the Lyapunov method. The key point to get the correct solution for axially moving continua is that the time derivation of an energy functional should be taken into account under Eulerian description with a physical concept. A novel way of deriving the time rate of change of the energy functional, then, is proposed.
