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