Understanding Lagrangian Mechanics

Hello friends! While studying Lagrangian mechanics( I have just started analytical mechanic a few weeks ago on my own just out of curiosity) , I was unable to understand what is the difference between dy and δy i.e. differential change in y and variation in y. Please help me in understanding this and also I want to know that what this calculus of variation is ?

#Mechanics

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$