In page-11 of I.E irodov Fundamental laws of mechanics, some notation used in the book is introduced. There, it is said that $\delta$ denotes the elementary value of a quantity but what exactly does elementary value of a quantity mean?
I'm confused as to what is meant by elementary value of a quantity.
This symbol is used in every theoretical mechanics book so we can look up other books for its definition. In Patrick Hamill's "A Student's Guide to Lagrangians and Hamiltonians", on page 11 it reads ($x_i$ and $q_\alpha$ are points' positions in old and new coordinates, $x_i=x_i(q_1,q_2,\cdots,q_n,t),$ $i=1,2,...,3N$ for $N$ points in $3$ dimension space),
"... we obtain $$dx_i=\sum_{\alpha=1}^{n}\frac{\partial x_i}{\partial q_\alpha}dq_\alpha+\frac{\partial x_i}{\partial t}dt.$$ But for a virtual displacement $\delta x_i$, time is frozen, so $$\delta x_i=\sum_{\alpha=1}^{n}\frac{\partial x_i}{\partial q_\alpha}dq_\alpha.$$ "
That is what it means. For other quantities, such as $\delta W$, the meaning is similar.
