>> >> >> The Euler-Lagrange Equations only specify when a
>> >> >> stationary condition occurs.
>> >> >
>> >> > What do you mean by "only"? What else do you need?
>> >>
>> >> Given a functon f(x), to find the minimum of this function, you solve
>> >> for x of the following.
>> >>
>> >> df(x)/dx = 0
>> >>
>> >> x only shows a stationary condition.  It is still up to your dilligence
>> >> to show
>> >>
>> >> d^2f(x)/dx^2 < 0
>> >>
>> >> In doing so, you can then claim a minimum of f(x).  This is as basic as
>> >> you can get.
>> >
>> > This is true except it's not relevant to this situation:
>>
>> You are wrong.  It is still relevant.
>
> No, it's not. You don't need the minimum to compute motion. Have you
> ever read a book on classical mechanics?

So, moving from point A to point B, if you don't need a minimum time
elapsed, then you can have an infinite number of ways to do so.  The
laws of physics exist because moving from point A to point B only
allows one path.