remark 20.11 What has no closed form, and what to do about it

open in the book · parts/03-classical-mechanics/03-exp-projectile-motion.tex:692 · p. 771

remark -- no derivation owed by its kind

Rests on

depends_on proposition 20.10 The descending branch is the steeper, whatever the resistive law ¶
- depends_on equation 20.10 eq:projectile-drag-eom ¶
- depends_on equation 20.6 eq:projectile-vertex ¶
- proves proof ch:03-exp-projectile-motion@proof-5 ¶
depends_on proposition 20.9 Linear resistance: exact motion, and the lost range ¶
- depends_on corollary 20.3 Range, apex, time of flight ¶
  - depends_on equation 20.5 eq:projectile-parametric ¶
  - depends_on theorem 20.2 Parabolic trajectory ¶
    - depends_on equation 18.7 eq:kin-const-acc-itinerary ¶
    - depends_on phenomenon 20.1 phen:parabolic-trajectory ¶
      - depends_on equation 18.7 eq:kin-const-acc-itinerary ¶ ↺
      - depends_on phenomenon 18.12 Uniformly accelerated motion ¶
    - depends_on postulate 19.8 Newton's second law ¶
      - depends_on definition 19.5 Linear momentum ¶
      - depends_on postulate 19.6 Newton's first law ¶
    - proves proof ch:03-exp-projectile-motion@proof-1 ¶
  - proves proof ch:03-exp-projectile-motion@proof-2 ¶
- depends_on corollary 9.9 Linear equations: existence on the whole interval ¶
  - depends_on definition 9.2 Linear equation; homogeneity ¶
    - depends_on definition 9.1 Ordinary differential equation ¶
  - depends_on remark 9.3 Normal form and first-order systems ¶
  - depends_on theorem 9.8 Picard–Lindelöf ¶
    - depends_on definition 9.4 Lipschitz condition ¶
    - depends_on equation 9.3 eq:slt-ode-system ¶
    - depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - proves proof ch:07-odes-sturm-liouville@proof-1 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-2 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-3 ¶
- depends_on equation 20.10 eq:projectile-drag-eom ¶ ↺
- proves proof ch:03-exp-projectile-motion@proof-4 ¶

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type	direction	node	provenance	where
`cites`	→	An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements	derived	parts/03-classical-mechanics/03-exp-projectile-motion.tex:704
`depends_on`	→	The descending branch is the steeper, whatever the resistive law	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:708
`depends_on`	→	Linear resistance: exact motion, and the lost range	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:708