Definition:Action (Dynamics)

This page is about action in the context of dynamics. For other uses, see action.

Definition

The action for a given segment from point $A$ to point $B$ on the trajectory of a dynamical system is defined by the line integral:

$\ds \sum_i \int_A^B p_i \rd q_i$

where:

$q_i$ are the generalized coordinates

$p_i$ are the generalized momenta.

Also see

• Results about action in the context of dynamics can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): action: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): action: 1.