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Topic: Landau & Lifschitz, Mechanics, Principle of Least Action
Replies: 10   Last Post: Jan 19, 2014 8:24 PM

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William Elliot

Posts: 1,233
Registered: 1/8/12
Re: Landau & Lifschitz, Mechanics, Principle of Least Action
Posted: Jan 18, 2014 10:59 PM
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> > 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.

> https://ia601205.us.archive.org/11/items/Mechanics_541/LandauLifshitz-Mechanics.pdf

References are 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.

> 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 q-dot(t) is implicitly defined as d/dt (delta q(t)).
> https://ia601205.us.archive.org/11/items/Mechanics_541/LandauLifshitz-Mechanics.pdf

References are useless.

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