Suppose that we have a function that depends on a path
. How does the function vary as the path is varied? Let
be a coordinate path and
be a varied path, where the function
is a path-like function that can be added to the path
, and the factor
is a scale factor. We define the variation
of the function
on the path
by
The variation of is a linear approximation to the change in the function
for small variations in the path. The variation of
depends on
.
— 1.5.1 Varying a path
— Structure and Interpretation of Classical Mechanics
.
Exercise 1.7. Properties of
The meaning of is
— Me@2019-04-27 07:02:38 PM
.
.
2019.04.27 Saturday ACHK