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



Re: Landau & Lifschitz, Mechanics, Principle of Least Action
Posted:
Jan 18, 2014 10:59 PM


> > 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/LandauLifshitzMechanics.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 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.



