Curvature in Terms of Two Derivatves

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Curvature in Terms of Two Derivatves
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13.3 4 Curvature of a Twisted Cubic
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13.3 Curvature of a Plane Curve
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13.3 5 Curvature of a Plane Parabola
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13.3 6 Normal (and Binormal)
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13.3 7 Eq of Normal Osculating Plane
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13.3 8 Graph the Osculating Circle
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M310 L10 13.4 Velocity and Acceleration in
Space

• Given position, find velocity, speed,
  acceleration.
• Given acceleration, find velocity and position,
  using initial conditions.
• Given position, find velocity, acceleration,
  force.
• Find max range of projectile.
• Tangential and normal components of acceleration.
• Keplers laws of planetary motion.

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13.4 6 Tangential and Normal Components of
Acceleration
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13.4 5 Maximizing Projectile Range
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13.4 Keplers Laws of Planetary Motion

• Planet follows elliptical orbit with sun at one
  focus
• Sun-planet line sweeps out area at a steady rate
• Square of period proportional to cube of s. m.
  axis

lead to the Inverse square law of gravitational
attraction