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Hint

1

Curvature Formula (not effiecent)

(x’(t)y’’(t)-x’’(t)y’(t))/(x’(t)²+y’(t)²)^(3/2)

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2

Efficient Curvature Formula

|r’(t)X r’’(t)|/|r’(t)|³

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3

Area Under Polar Curve

A = (1/2) ∫[a, b] r^2 dθ

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4

Cartesian to Cylinderical Conversions

x=rcos(theta)sin(phi)

y=rsin(theta)sin(phi)

z=rcos(phi)

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5

Second Derivative of Parametric with Respect to x

(x’(t)y’’(t)-x’’(t)y’(t))/x’(t)³

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6

Projection of u onto v

((u*v)/(v*v))**v**

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7

T(t)

r’(t)/|r’(t)|

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8

N(t)

T’(t)/|T’(t)|

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9

Decomposition of Acceleration

a=a(t)T+a(n)N

a(t)=v’(t)

a(n)=K(t)v(t)²

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10

Point to Line Distance

**u**=(r-p)-((r-p)***v**)**v**

r= start point

p= point on line

v= directional vector of line

|**u**| = distance

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11

Point to Plane Distance

**u**=((p-r)***n**)**n**

r= start point

p= point on plane

**n**= normal vector

|**u**| = distance

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