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feat(HJ): Chapter 3 — Advanced Analytical Mechanics (Hamilton-Jacobi)

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Add Chapter 3 with 13 concept files covering:
- HJ Fundamentals: derivation, separation, action-angle, EM coupling
- Mechanics problems: free particle, projectile, SHO, Kepler, rigid rotator
- EM problems: uniform E-field, cyclotron, E×B drift, Coulomb

Also: manifest update (13 entries), macro additions (HJ + \bm + \dd override),
unicode cleanup, compilation fixes.
This commit is contained in:
Krishna Ayyalasomayajula
2026-05-02 02:21:53 -05:00
parent 7cf82f52da
commit 1c1a575f6e
22 changed files with 3048 additions and 7 deletions
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13
macros.tex
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@@ -31,3 +31,16 @@
\newcommand{\sol}{\setlength{\parindent}{0cm}\textbf{\textit{Solution:}}\setlength{\parindent}{1cm} }
\newcommand{\solve}[1]{\setlength{\parindent}{0cm}\textbf{\textit{Solution: }}\setlength{\parindent}{1cm}#1 \Qed}
% === Hamilton-Jacobi notation ===
\newcommand{\Sdel}[1]{\pdv{S}{#1}}
\newcommand{\Sdelo}[2]{\pdv[#1]{S}{#2}}
\newcommand{\Jact}[1]{J_{#1}}
\newcommand{\wangle}[1]{w_{#1}}
\newcommand{\sepconst}[1]{\alpha_{#1}}
\newcommand{\pbracket}[2]{\left\{#1,#2\right\}}
\newcommand{\Lagrian}{\mathcal{L}}
\newcommand{\bm}[1]{\mathbf{#1}}
% === Safe differentials for Advanced chapter (no \@ifnextchar) ===
\renewcommand{\dd}{\mathrm{d}}