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SYSTEMS OF ODES Consider the pendulum shown below. Assume the rod
 

Summary: SYSTEMS OF ODES
Consider the pendulum shown below. Assume the rod
is of neglible mass, that the pendulum is of mass m,
and that the rod is of length `. Assume the pendulum
moves in the plane shown, and assume there is no
friction in the motion about its pivot point. Let (x)
denote the position of the pendulum about the vertical
line thru the pivot, with measured in radians and x
measured in units of time. Then Newton's second
law implies
m`
d2
dx2
= mg sin ( (x))
Introduce Y1(x) = (x) and Y2(x) = 0(x). The
function Y2(x) is called the angular velocity. We can
now write
Y 0
1(x) = Y2(x); Y1(0) = (0)
Y 0

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences