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The $\delta$ notation in Goldstein's Classical Mechanics on the calculus of variation
In Goldstein's classical mechanics (page 36) he introduces the basics of the calculus of variation and uses it to effectively the Euler-Lagrange equations. However, there is a step in which the $\...
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The use of $x_\varepsilon (t) = x(t) + \varepsilon (t)$ and $x_\varepsilon (t) = x(t) + \varepsilon \eta (t)$ in proving Hamilton's principle
The following Wikipedia page uses $x_\varepsilon (t) = x(t) + \varepsilon (t)$ in the proof.
https://en.wikipedia.org/wiki/Hamilton%27s_principle#Mathematical_formulation
But in my mechanics book (by ...
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How do physicists know when it is appropriate to use $\mathrm dx$ as if it is a number? [duplicate]
I'm trying to teach myself calculus of variations when I came across a worked example about the shortest distance between two points in a plane. This is a question about the mathematics but I don't ...
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$\int (f(x+\delta x) - f(x)) dx = \int \left ( \frac{df(x)}{dx} \delta x \right) dx$
From Landau and Lifshitz's Mechanics Vol: 1
$$
\delta S= \int \limits_{t_1}^{t_2} L(q + \delta q, \dot q + \delta \dot q, t)dt - \int \limits_{t_1}^{t_2} L(q, \dot q, t)dt \tag{2.3b}$$
$$\Rightarrow ...
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