![\displaystyle{\mathcal{F} [\gamma]}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B%5Cmathcal%7BF%7D+%5B%5Cgamma%5D%7D&bg=ffffff&fg=333333&s=0 "\displaystyle{\mathcal{F} [\gamma]}")
……….It may depend upon the value of the function 
……….and the value of any derivatives of
.
We can decompose ![\mathcal{F} [\gamma]](https://s0.wp.com/latex.php?latex=%5Cmathcal%7BF%7D+%5B%5Cgamma%5D&bg=ffffff&fg=333333&s=0 "\mathcal{F} [\gamma]")
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}}](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle%7B+%5Cbegin%7Baligned%7D++%5Cmathcal%7BF%7D+%5B%5Cgamma%5D+%26%3D+%5Cmathcal%7BL%7D+%5Ccirc+%5Cmathcal%7BT%7D%5B%5Cgamma%5D+%5C%5C++%5Cmathcal%7BT%7D+%5B%5Cgamma%5D+%26%3D+%28t%2C+%5Cgamma+%28t%29%2C+%5Cmathcal%7BD%7D+%5Cgamma+%28t%29%2C+...%29++%5Cend%7Baligned%7D%7D&bg=ffffff&fg=333333&s=0 "\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
.
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2019.02.24 Sunday ACHK
