Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 42 - 1923  

Research Article

The Conservation Theorems of a Damped Dynamical System

E. T. Copson

The Partial Differential Equations of Physics may be defined as those equations which can be derived from a “least action principle,” that is, as those which are obtained by making a certain integral stationary by the methods of the Calculus of Variations. But, generally speaking, such equations belong to conservative physical systems, and not to those which involve dissipation of energy. In this note it is shewn that a certain class of dissipative equation, of which the best known example is the equation of telegraphy, can be derived from such a calculus of variations problem.

(Received May 01 1923)

(Accepted March 07 1923)