Quadric Surfaces
(x/2)^2+(y/3)^2+(z/4)^2=1
What is the equation of an ellipsoid?
vec n cdot <x, y, z> = d
What is the equation of a plane in 3 space?
The simplest example of: v(t) is constant but the direction of vec v is changing
What is uniform circular motion?
Figured out that the planetary orbits are elliptical
Who was Johannes Kepler?
<x'(t), y'(t), z'(t)>
What is the tangent or velocity vector?
z=(x/3)^2+(y/4)^2
What is the equation of an elliptic paraboloid?
What vec u cdot vec v < 0 means for theta
What is an obtuse angle?
(vec v(t))/(||vec v(t)||)
What is
vec T ?
What is a geosynchronous orbit?
sqrt((x')^2+(y')^2+(z')^2
What is the speed?
y=3x^2
What is the equation of a parabolic cylinder?
The connection between || vec u xx vec v || and area
How can you find the area of a parallelogram?
(vec T'(t))/(|| vec T'(t)||
What is
vec N(t) ?
vec F(vec r(t))=-((k m)/(||vec r||^2))vec e_r
What is Newton's Universal Law of Gravitation?
int sqrt((x')^2+(y')^2+(z')^2) dt
What is the arc length or path length?
(x/2)^2+(y/3)^2-(z/4)^2=1
What is the equation of a hyperboloid of 1 sheet?
The connection between | vec u cdot (vec v xx vec w) | and geometry
How can you find the volume of a parallelepiped?
v'(t) = vec a cdot vec T
What is
a_T ?
(d(Area))/dt is constant
What is Kepler's 2nd Law or "equal area in equal time" ?
|f''(x)|/(1+f'(x)^2)^(3/2)
How do you find curvature in the plane?
(x/2)^2+(y/3)^2-(z/4)^2= -1
What is the equation of a hyperboloid of 2 sheets?
What (vec u cdot vec v)/(vec v cdot vec v) vec v gives you
What is the projection of vector u along vector v ?
k(t) v(t)^2
What is
a_N ?
T^2=((4 pi^2)/(G M)) a^3
What is Kepler's 3rd law or Kepler's Law of the Period ?
||r'(t) xx r''(t)||/||r'(t)||^3
How do you find curvature in 3D?