Lagrangian system

In mathematics, a Lagrangian system is a pair $(Y, L)$ , consisting of a smooth fiber bundle $Y \to X$ and a Lagrangian density $L$ , which yields the Euler–Lagrange differential operator acting on sections of $Y \to X$ .

In classical mechanics, many dynamical systems are Lagrangian systems. The configuration space of such a Lagrangian system is a fiber bundle $Q \to ℝ$ over the time axis $ℝ$ . In particular, $Q = ℝ \times M$ if a reference frame is fixed. In classical field theory, all field systems are the Lagrangian ones.

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