equation 19.4 eq:newt-fma

Rests on

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Supports

• depends_on definition A.658 The orbit function ¶
  • depends_on definition A.659 Circular orbit and its index ¶
    • depends_on lemma A.660 The index in terms of the force ¶
      • depends_on proposition A.661 The first-order narrowing ¶
        • depends_on theorem A.664 Bertrand's condition ¶
• depends_on phenomenon 19.10 Force, mass and acceleration ¶
• depends_on proposition 19.71 The Newtonian closed system is a Lagrangian system ¶
• depends_on theorem 27.30 Reduction of the two-body problem ¶
  • depends_on phenomenon 27.32 Kepler's first law: bound orbits are closed ellipses ¶
  • depends_on phenomenon 27.35 Kepler's third law ¶
    • depends_on phenomenon 50.5 Black-hole masses from gravitational waves ¶
    • depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶
    • depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶
  • depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶ ↺
  • depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶ ↺
• depends_on theorem 19.32 Conservation of energy ¶
  • depends_on phenomenon 50.6 No material surface ¶
  • depends_on phenomenon 19.33 Mechanical energy is conserved ¶
  • depends_on theorem 21.43 Conservation of energy ¶
    • depends_on proposition 29.36 Three first integrals ¶
      • depends_on phenomenon 29.38 Nutation of a released top ¶
      • depends_on proposition 29.43 The three integrable heavy tops ¶
        • depends_on remark 29.45 What integrability buys, and where it stops ¶
        • depends_on remark 29.44 The Kovalevskaya integral ¶
      • depends_on proposition 29.40 The sleeping top ¶
      • depends_on theorem 29.37 Reduction to one degree of freedom ¶
        • depends_on phenomenon 29.38 Nutation of a released top ¶ ↺
        • depends_on proposition 29.40 The sleeping top ¶ ↺
        • depends_on remark 29.42 The closed form, and the mathematics it needs ¶
    • depends_on theorem 27.10 Lagrange–Dirichlet ¶
• depends_on theorem 19.12 Galilean covariance of the second law ¶
  • depends_on proposition 19.13 Which forces are admissible ¶
    • depends_on corollary 19.14 Central pair forces are admissible ¶
      • depends_on postulate 19.61 Newton's third law, strong form ¶
        • depends_on theorem 19.63 The spin obeys the same law about the centre of mass ¶
        • depends_on theorem 19.62 Rotational second law for a system ¶
  • depends_on theorem 19.25 Galilean covariance of the rotational second law ¶
• depends_on theorem 19.38 Work–energy theorem ¶
• step_from equation 27.26 eq:cfs-energy-conserved ¶
• step_from equation 27.44 eq:cfs-relative-derivation ¶