proposition 20.9 Linear resistance: exact motion, and the lost range

open in the book · parts/03-classical-mechanics/03-exp-projectile-motion.tex:523 · p. 770

Rests on

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 definition 18.11 Acceleration ¶
      - depends_on equation 18.7 eq:kin-const-acc-itinerary ¶ ↺
      - proves proof ch:01-kinematics@proof-1 ¶
  - depends_on postulate 19.8 Newton's second law ¶
    - depends_on definition 19.5 Linear momentum ¶
      - depends_on definition 18.10 Velocity ¶
      - depends_on definition 19.3 Mass ¶
    - depends_on postulate 19.6 Newton's first law ¶
      - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 19.5 Linear momentum ¶ ↺
  - 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 definition 7.16 Limit ¶
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
    - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - depends_on corollary A.46 Monotone convergence ¶
      - depends_on definition 7.45 Series ¶
      - depends_on theorem 7.8 Cauchy criterion ¶
      - proves proof ch:05-real-analysis@proof-28 ¶
    - 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 ¶

Supports

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

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
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Edges

type	direction	node	provenance	where
`depends_on`	→	Range, apex, time of flight	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:549
`depends_on`	→	Linear equations: existence on the whole interval	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:549
`depends_on`	→	eq:projectile-drag-eom	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:549
`depends_on`	←	What has no closed form, and what to do about it	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:708
`proves`	←	ch:03-exp-projectile-motion@proof-4	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:553