Tuesday, March 12, 2013

The Hodograph and Mamikon's Theorem

Just a quick note today on a fun article[1] and a new word, (hodograph), I found in the American Mathematical Monthly journal from the +Mathematical Association of America .  The article uses Mamikon's theorem to prove Kepler's second law.  Mamikon's theorem states that the area swept out by the velocity, (tangent), vector to a parameterized position position curve is the same as the area swept out by the same set of velocity vectors if you laid them out with a their tails all placed at a common center.  The curve swept out by all the velocity vectors with their tails placed at the same point is called the hodograph and was defined by W. R. Hamilton.  The hodograph in this scenario defines the acceleration curve for the particle!  Haimlton's article defining the hodograph can be found freely available at http://www.jstor.org/stable/20489607. [2]





References:
(2013). Visual Angular Momentum: Mamikon Meets Kepler, The American Mathematical Monthly, 120 (1) 71-73. DOI:


2.  Hamilton's hodograph article
http://www.jstor.org/stable/20489607

Articles to come back to:
Notes on matrix theory
http://www.jstor.org/stable/2310556

No comments: