Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Action (physics)
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
=== Abbreviated action (functional) === <!-- [[Symplectic action]] redirects here -->{{anchor| Symplectic action}}{{anchor| abbreviated action}} In addition to the action functional, there is another functional called the ''abbreviated action''. In the abbreviated action, the input function is the ''path'' followed by the physical system without regard to its parameterization by time. For example, the path of a planetary orbit is an ellipse, and the path of a particle in a uniform gravitational field is a parabola; in both cases, the path does not depend on how fast the particle traverses the path. The abbreviated action <math>\mathcal{S}_{0}</math> (sometime written as <math>W</math>) is defined as the integral of the generalized momenta, <math display="block">p_i = \frac{\partial L(q,t)}{\partial \dot{q}_i},</math> for a system Lagrangian <math>L</math> along a path in the [[generalized coordinates]] <math>q_i</math>: <math display="block"> \mathcal{S}_0 = \int_{q_1}^{q_2} \mathbf{p} \cdot d\mathbf{q} = \int_{q_1}^{q_2} \Sigma_i p_i \,dq_i. </math> where <math>q_1</math> and <math>q_2</math> are the starting and ending coordinates. According to [[Maupertuis's principle]], the true path of the system is a path for which the abbreviated action is [[stationary point|stationary]].
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)