
#1
Sep913, 05:49 PM

P: 177

Hello All,
I have been reading this thread, trying to understand the concept of action. There is one very intriguing (to me) statement in that thread: "So your action is the difference between your capability of motion and your actual motion. The principle of least action says that there is no difference without some sort of constraint  in which case the motion will be such that this difference is as small as possible." /by Simon Bridge/ Do I understand this correctly  the action is always zero for unconstrained motion; and never zero (but minimal) for constrained motion. Is this reasoning true? Is free fall a constrained motion? Because the action is zero only at y = y_initial / 2, y is the vertical position. Perhaps someone has an idea... 



#2
Sep1013, 02:45 AM

Thanks
P: 1,294

See the Feynman lecture on "Least Action" ... it is best to get a complete overview. Otherwise you may never see the forest for the trees!
http://liberzon.csl.illinois.edu/tea...hapter219.pdf 



#3
Sep1013, 02:59 PM

P: 177

Thank you, UltrafastPED; I read the chapter you suggested. Quite a few good points there. I am still having trouble to understand something, though. What is "zero action"? Does it have any significance?
In the chapter by Feinman, the free falling body moves downwards and its lagrangian changes from negative to positive. At some point (half the initial height), it becomes zero. Does this zero lagrangian have any physical significance? 



#4
Sep1013, 05:39 PM

Mentor
P: 16,470

What is "zero action"
The actual value of the action is not important, only that it is minimized. The value of the action can be made arbitrarily large or small simply by adding a constant offset to the potential.




#5
Sep1213, 02:39 PM

P: 177

What if, in a system, E_{p} = f(x)  C, C is arbitrary constant E_{k} = f(x) for all x. Then L = E_{k}  E_{p} = C for all x, thus the action remains constant. Does this ever happen? 



#6
Sep1213, 05:36 PM

Mentor
P: 16,470

In principle, it is possible, but I have never seen such a system. Usually the potential energy is a function of the generalized positions and the kinetic energy is a function of the generalized velocities, so I haven't seen a case where they are the same functions like that.



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