24 | February | 2019 | Physics Town

$\displaystyle{\gamma(t)}$ = 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

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Physics Town

continues

Daily Archives: February 24, 2019

知識論

Path-distinguishing function, 2