example A.572 Rotational reduction of the central-force problem

Rests on

• depends_on equation 27.32 eq:cfs-effective-potential ¶
• depends_on example 24.44 Linear and angular momentum ¶
  • depends_on definition 24.43 Momentum map ¶
    • depends_on definition 14.2 Lie group ¶
    • depends_on definition 24.14 Hamiltonian vector field ¶
      • depends_on definition 24.8 Symplectic manifold ¶
        • depends_on definition 13.105 Closed form ¶
        • depends_on definition 13.98 $k$-form ¶
        • depends_on definition 24.2 Symplectic vector space ¶
      • depends_on equation 22.4 eq:ham-pdot ¶
      • depends_on equation 22.3 eq:ham-qdot ¶
    • depends_on definition 24.17 Symplectomorphism ¶
      • depends_on definition A.70 Pullback ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶
        • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.98 $k$-form ¶ ↺
      • depends_on definition 24.8 Symplectic manifold ¶ ↺
  • depends_on equation 24.3 eq:sym-canonical-forms ¶
• depends_on theorem A.563 Marsden–Weinstein reduction ¶
  • depends_on definition A.561 Coadjoint action and equivariance ¶
    • depends_on definition 4.21 Group ¶
      • depends_on definition 4.11 Inverse element ¶
        • depends_on definition 4.9 Neutral element ¶
      • depends_on definition 4.20 Monoid ¶
        • depends_on definition 4.9 Neutral element ¶ ↺
        • depends_on definition 4.18 Semigroup ¶
    • depends_on definition 14.2 Lie group ¶ ↺
    • depends_on definition 24.43 Momentum map ¶ ↺
  • depends_on lemma 24.46 The level set of the momentum map is the symplectic orthogonal of the orbit ¶
    • depends_on definition 24.8 Symplectic manifold ¶ ↺
    • depends_on definition 24.43 Momentum map ¶ ↺
    • depends_on theorem 13.59 Regular value theorem ¶
      • depends_on definition 13.52 Differential; pushforward ¶
        • depends_on definition 13.49 Smooth map between manifolds ¶
        • depends_on definition 13.81 Vector on a manifold ¶
      • depends_on definition 13.58 Hypersurface ¶
        • depends_on definition 13.54 Embedded submanifold ¶
      • depends_on definition 13.49 Smooth map between manifolds ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-10 ¶
    • proves proof ch:07-symplectic-geometry@proof-15 ¶
  • depends_on theorem 13.67 Quotient manifold theorem ¶
    • depends_on definition 13.66 Smooth action; free; proper; orbit ¶
      • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.47 Differentiable structure ¶
      • depends_on definition 13.49 Smooth map between manifolds ¶ ↺
      • depends_on definition 6.9 Compact set ¶
        • depends_on definition 6.5 Open cover ¶
    • depends_on definition 13.54 Embedded submanifold ¶ ↺
    • depends_on theorem 13.63 Constant rank theorem ¶
      • depends_on corollary A.292 Inverse function theorem ¶
        • depends_on proposition 7.104 Chain rule in several variables ¶
        • depends_on theorem A.286 Implicit function theorem ¶
        • proves proof app:A-long-proofs@proof-186 ¶
      • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶ ↺
      • depends_on theorem A.286 Implicit function theorem ¶ ↺
      • proves proof ch:11-manifolds-tensors-curvature@proof-12 ¶
    • proves proof app:A-long-proofs@proof-329 ¶
    • proves proof ch:11-manifolds-tensors-curvature@prooflink-2 ¶
  • proves proof app:A-long-proofs@proof-346 ¶

Supports

Nothing declares a dependency on this node yet.