This comes from Wiki. I just liked this description for distinction between Eulerian and Lagrangian.
—————————————————————–
This static position derivative is called the Eulerian derivative.
An example of this case is a swimmer standing still and sensing temperature change in a lake early in the morning: the water gradually becomes warmer due to heating from the sun.
If, instead, [...]
Archive for the ‘Classical Mechanics’ Category
Material Derivative(Lagrangian)
Posted in Classical Mechanics on October 13, 2008 | Leave a Comment »
Adiabatic Invariant
Posted in Classical Mechanics on April 26, 2008 | Leave a Comment »
It seems adiabatic invariant is important to analyze and understand physics of nature heuristically like magnetic moment which is usually assumed as a conserved quantity in plasma physics field. To understand adiabatic invariant in the structure of classical mechanics, we need to deal with some theory.
This article is written to understand more deeply where adiabatic quantities [...]
Pullback
Posted in Classical Mechanics on March 18, 2008 | Leave a Comment »
<Wiki>
The notion of pullback in mathematics is a fundamental one. It refers to two different, but related processes: precomposition and fiber-product.
Precomposition with a function probably provides the most elementary notion of pullback: in simple terms, a function f of a variable y, where y itself is a function of another variable x, may be written [...]
Geometry Reference Books
Posted in Classical Mechanics on March 15, 2008 | Leave a Comment »
I’ve been tried to figure out differentiail geometry to use for gyrokientics. However, it was hard to find a book easily and readably describing all contents for non-mathematician. In addition, sometimes each book has their own notations or describes a same thing with other words or definition, which makes me more hard to understand geometry.
It’s just reference books I’ve read. The description [...]
Symplectic manifolds
Posted in Classical Mechanics on March 15, 2008 | Leave a Comment »
<Wiki>
In mathematics, a symplectic manifold is a smooth manifold M equipped with a closed, nondegenerate, 2-form ω called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds, e.g. in the [...]
