14 - interval t where F is continuous and F t (except...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
f F t = f F t = f t F t (scalar function times vector function) F x G t = F t x G t F G t = blah blah blah. ..all operations pretty much work You can even stick limits on both sides. Continuity is defined the same way as before. Thm 14.2.3: If the nonzero vector F (t) is differentiable and has constant length, then F (t) is orthogonal to F’ (t). (If you have a unit vector, it is necessarily of constant length.) F t d t = f 1 t d t , f 2 t d t , f 3 t d t C , where C = C 1 , C 2 , C 3 . Since T is the unit tangent vector d T d s only measures the change in direction. Direction of motion is the unit velocity vector. Graph of the position vector is the trajectory. Note velocity V t = speed direction = V V V . A graph of a vector function is smooth on an
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: interval t where F is continuous and F t (except possibly at endpoints of the interval). Newtons Second Law : F t = m a t Consider coordinate system with the sun at the origin (ignore all other planets): you get Newtons Law of Gravitiation F = GMm r 3 r = GMm r 2 u , where u is a unit vector and r = r , F is the force vector of the planet, and r is the position vector of the planet. Thm 14.4.1 A polar eqn of form r = ed 1 e cos or r = ed 1 e sin represents a conic section. The conic section is an ellipse if e 1, parabola if e = 1 and hyperbola if e 1....
View Full Document

This note was uploaded on 04/14/2008 for the course MATH 252 taught by Professor Bumpus during the Fall '07 term at Austin College.

Ask a homework question - tutors are online