Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


Hetware
Posts:
148
Registered:
4/13/13


Re: Landau & Lifschitz, Mechanics, Principle of Least Action
Posted:
Jan 19, 2014 11:05 AM


On 1/18/2014 10:59 PM, William Elliot wrote: >>> It comes of the general definition in use, namely. >>> delta f(x) = f(x + delta x)  f(x) >> >> That is NOT the definition of delta f(x) in use. This is variational calculus >> not traditional differential calculus. > > What? It's a calculus of variation problem? Not by what you wrote.
Even if you are unfamiliar with "Landau & Lifschitz, Mechanics", the part about "Principle of Least Action" clearly frames the discussion as pertaining to variational dynamics.
>> https://ia601205.us.archive.org/11/items/Mechanics_541/LandauLifshitzMechanics.pdf >> > References are useless.
A link to the text under discussion is useless?
>> "Let q=q(t) be the function for which S is a minimum. This means that S is >> increased when q(t) is replaced by any function of the form >> > What's S? > >> q(t) + delta q(t), (2.2) >> where delta q(t) is a function which is small everywhere in the interval of >> time from t_1 to t_2; delta q(t) is called a /variation/ of the function q(t). > >> Since for t=t_1 and for t=t_2, all function (2.2) must take values q^(1) and >> q^(2) respectively, it follows that > > What does "^(1)" mean.
It appears the authors assumed its meaning to be clear from context. It's obvious to me that it is a designation for q[t_1]. I don't know why they chose that notation. I merely reproduced it.
>> delta q(t_1) = delta q(t_2) = 0." >> >> To be pedantic, they also need some caveats about differentiability >> >> The first equation on page 3 (not page 2, as I originally indicated) is where >> delta qdot(t) is implicitly defined as d/dt (delta q(t)). >> >> https://ia601205.us.archive.org/11/items/Mechanics_541/LandauLifshitzMechanics.pdf >> > References are useless. >
In your experience, I trust that they are useless.



