Path-distinguishing function, 2

\displaystyle{\gamma(t)} = configuration path function

\displaystyle{\mathcal{F} [\gamma]} = a function of time that measures some local property of the path

……….It may depend upon the value of the function \displaystyle{\gamma} at that time

……….and the value of any derivatives of \displaystyle{\gamma} at that time.

.

We can decompose \mathcal{F} [\gamma] into two parts:

1. a part that measures some property of a local description

and

2. a part that extracts a local description of the path from the path function.

.

— 1.3 The Principle of Stationary Action

— Structure and Interpretation of Classical Mechanics

.

1. The function that measures the local property of the system depends on the particular physical system;

2. the method of construction of a local description of a path from a path is the same for any system.

.

\displaystyle{ \begin{aligned}  \mathcal{F} [\gamma] &= \mathcal{L} \circ \mathcal{T}[\gamma] \\  \mathcal{T} [\gamma] &= (t, \gamma (t), \mathcal{D} \gamma (t), ...)  \end{aligned}}

.

— 1.3 The Principle of Stationary Action

— Structure and Interpretation of Classical Mechanics

— Me@2019-02-22 11:46:50 PM

.

.

2019.02.24 Sunday ACHK