1. Systems of More Than One Particle into the frying pan, with subscripts 1 Multi-body Systems

2. Comments on Forces Many types of force are not fundamental: friction drag upward force of a floor They are due to interactions between atoms. Multi-body Systems 2

3. More on Forces Fundamental forces act between particles: gravitational force electric forces They depend upon properties of the particles (mass, charge) which are part of each particle’s specification the location of all of the particles Multi-body Systems 3

4. What Determines the Forces? Multi-body Systems 4

5. 5

6. Configuration Space Multi-body Systems 6

7. State Space Multi-body Systems 7

8. Phase Space Multi-body Systems 8

9. More Phase Space We refer to the 6N-dimensional space of positions and momenta as phase space. So far we’ve seen configuration space – position state space – position and velocity phase space – position and momentum That’s as far as we’ll need to go. Multi-body Systems 9

10. Phase Space Equations of Motion Multi-body Systems 10

11. Isaac Newton’s Third Law For every action there is an equal and opposite reaction. How do we take account of this? Multi-body Systems 11

12. Third Law (cont.) Multi-body Systems 12

13. Conserving Momentum Multi-body Systems 13

14. Still Conserving Momentum Multi-body Systems 14