lemma 27.15 Velocity and acceleration in plane polar coordinates

open in the book · parts/03-classical-mechanics/10-central-forces-statics.tex:400 · p. 929

Rests on

depends_on definition 18.11 Acceleration ¶
- depends_on definition 7.26 Derivative of a function 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 definition 3.43 Map ¶
  - depends_on definition 7.9 Real function ¶ ↺
- depends_on definition 18.10 Velocity ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
  - depends_on definition 18.9 Position ¶
    - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.3 Particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
  - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 13.8 Curve ¶
depends_on definition 18.10 Velocity ¶ ↺
depends_on proposition 7.31 Chain rule ¶
- depends_on definition 7.13 Composite function ¶
  - depends_on definition 7.9 Real function ¶ ↺
- depends_on proposition 7.27 Differentiable implies 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 definition 7.26 Derivative of a function at a point ¶ ↺
  - depends_on proposition 7.6 Algebra of limits ¶
    - depends_on definition 7.4 Convergence ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
    - depends_on proposition 7.3 Triangle inequality ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
      - proves proof ch:05-real-analysis@proof-1 ¶
    - proves proof ch:05-real-analysis@proof-3 ¶
  - proves proof ch:05-real-analysis@proof-11 ¶
- depends_on proposition 7.6 Algebra of limits ¶ ↺
- proves proof ch:05-real-analysis@proof-15 ¶
proves proof ch:10-central-forces-statics@proof-7 ¶

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type	direction	node	provenance	where
`depends_on`	→	Acceleration	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:419
`depends_on`	→	Velocity	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:419
`depends_on`	→	Chain rule	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:419
`proves`	←	ch:10-central-forces-statics@proof-7	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:423