example 21.74 Rindler coordinates

open in the book · parts/03-classical-mechanics/04-lagrangian-mechanics.tex:2162 · p. 800

example -- no derivation owed by its kind

Rests on

depends_on equation 21.75 eq:lag-geodesic ¶
depends_on equation 21.85 eq:lag-rindler-metric ¶
depends_on theorem 13.152 Riemann tensor; Ricci identity with torsion ¶
- depends_on definition 13.145 Affine connection ¶
  - depends_on definition 13.90 Mixed tensor ¶
    - depends_on definition 13.89 Contravariant and covariant tensors ¶
      - depends_on definition 13.88 General coordinate transformation ¶
    - depends_on definition 13.88 General coordinate transformation ¶ ↺
  - depends_on definition 13.82 Vector field ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶
- depends_on definition 13.147 Torsion ¶
  - depends_on definition 13.145 Affine connection ¶ ↺
- depends_on proposition 7.105 Clairaut–Schwarz ¶
  - depends_on definition 7.20 Continuity at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.7 eq:ana-limit-left ¶
    - depends_on equation 7.5 eq:ana-limit-right ¶
  - depends_on theorem 7.35 Mean value theorem ¶
    - depends_on proposition 7.29 Linearity ¶
      - depends_on definition 7.11 Sum of functions ¶
      - depends_on equation 7.14 eq:ana-derivh ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-13 ¶
    - depends_on theorem 7.34 Rolle ¶
      - depends_on lemma 7.33 Fermat: interior extremum ¶
      - depends_on theorem 7.24 Extreme value theorem ¶
      - proves proof ch:05-real-analysis@proof-18 ¶
    - proves proof ch:05-real-analysis@proof-19 ¶
  - proves proof ch:05-real-analysis@proof-64 ¶
- proves proof ch:11-manifolds-tensors-curvature@proof-42 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	eq:lag-geodesic	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:2237
`depends_on`	→	eq:lag-rindler-metric	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:2237
`depends_on`	→	Riemann tensor; Ricci identity with torsion	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:2237