Sept. 14, 2004 --- Class 5 ---Newton's Laws of Motion, Energy Nonconservation
Activities:
Solving Newton's Law of Motion
We started Chapter 3 and discussed how to turn a 2nd order
differential equation into a series of coupled first order
differential equations. We also discussed why position,
velocity and acceleration are so important, and the next
derivative, called the jerk, is not well known.
The program fall1.c in ~sg contains code to integrate the
equations for a falling body. It is set up for the
Euler algorithm. We discussed the code in detail.
If the lines for updating v and y are
reversed, you get the Euler-Cromer algorithm. In the next
class we will discuss the Euler-Richardson algorithm, and
explore the step size dependence of the trajectory of a
falling body. We talked about energy conservation and
how to write an awk expression to calculate the energy.
We studied the energy of a falling body as caculated by the
Euler algorithm. We looked at the energy at t = 1 sec.
We also created a shell script to automate the procedure:
#!/bin/csh
# this is the best shell script I have ever written
foreach step ( 0.025 0.05 0.1 0.2)
fall1 <