equation 22.1 eq:ham-hamiltonian
open in the book ·
parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:70
- part of a statement or proof
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Supports
- depends_on definition 32.57 The Hénon–Heiles Hamiltonian ¶
- depends_on definition 32.46 The circular restricted three-body problem ¶
-
depends_on
proposition 22.11
Hamiltonian and total energy
¶
- depends_on remark 22.12 The hypothesis, stated sharply ¶
- depends_on remark 22.13 Euler's theorem on homogeneous functions is owed ¶
-
depends_on
proposition 23.7
The principal function is the action
¶
- depends_on remark 23.8 The action as a function, not a functional ¶
-
depends_on
remark 22.5
Units
¶
- depends_on remark 22.36 The whole dynamics in one operation ¶
- depends_on remark 22.42 What the matrix form is for ¶
-
depends_on
remark 24.11
The SI dimension of every object in this chapter
¶
- depends_on remark 24.35 What non-squeezing does and does not say about nature ¶
- depends_on remark 24.22 Liouville's theorem is the foundation of statistical mechanics ¶
-
depends_on
remark 24.27
Fixing a scale, so that a ``ball'' means something
¶
-
depends_on
definition 24.28
Ball and cylinder
¶
- depends_on definition 24.33 Symplectic capacity ¶
- depends_on example 24.29 A volume-preserving squeeze ¶
- depends_on proposition 24.30 Linear non-squeezing ¶
- depends_on theorem 24.31 Gromov's non-squeezing theorem ¶
- depends_on definition 24.33 Symplectic capacity ¶ ↺
-
depends_on
definition 24.28
Ball and cylinder
¶
- step_from equation 22.7 eq:ham-dH ¶
Neighborhood
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
← | The Hénon–Heiles Hamiltonian | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1505 |
depends_on |
← | The circular restricted three-body problem | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:1179 |
depends_on |
← | Hamiltonian and total energy | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:310 |
depends_on |
← | The principal function is the action | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:262 |
depends_on |
← | Units | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:142 |
step_from |
← | eq:ham-dH | declared — the two terms in $\dd\dot{q}^{a}$ cancel | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:188 |