Invariance of Euler-Lagrange Equations

E-L is deduced from the Hamilton’s principle

$$\delta S=\delta\int L(\bm q, \dot{\bm q}, t)dt …
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Jacobi Identity for Classical Possion Bracket

Definition of Classical Possion Bracket:

$$[f, g]=\sum_{i=1, 2,\ldots, n}\frac{\pp(f, g)}{\pp …
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From d’Alembert to Lagrange

Nowtonian

Assume \(\bm F\) is active force and \(\bm R\) is constraint force. Then for …

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Integrable Constraint

In N dimension,

$$\begin{aligned} \bm f\times\bm g&\rightarrow f_a\times g_b=[f_ag_b]_{ab}\\ \bm f …
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