Relativistic-Covariant Lagrangian Formalism

Abstract

In this chapter we want to discuss the relativistic-covariant formulation of the Lagrange equation of Mechanics. Therefore, we will remind the reader briefly of the essential aspects of the Lagrangian formulation of point mechanics. This theory is based on Hamilton’s principle. It tells us that the time integral over the Lagrange function $L({q_1},{q_2}, \ldots ;{\dot q_1},{\dot q_2}, \ldots ;t)$ should be an extreme value, that is,

$$ \delta \int_{{t_1}}^{{t_2}} {dtL({q_1},{q_2}, \ldots ;{{\dot q}_1},{{\dot q}_2}, \ldots ;t)} = 0 $$

(23.1)