1. 9/19/2012PHY 711 Fall 2012 -- Lecture 101 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 10: Continue reading Chapter 3 & 6 1.Summary & review 2.Lagrange’s equations with constraints

2. 9/19/2012PHY 711 Fall 2012 -- Lecture 102

3. 9/19/2012PHY 711 Fall 2012 -- Lecture 103

4. 9/19/2012PHY 711 Fall 2012 -- Lecture 104

5. 9/19/2012PHY 711 Fall 2012 -- Lecture 105 Comment on problem set #6 s

6. 9/19/2012PHY 711 Fall 2012 -- Lecture 106

7. 9/19/2012PHY 711 Fall 2012 -- Lecture 107 Comments on generalized coordinates: Here we have assumed that the generalized coordinates q  are independent. Now consider the possibility that the coordinates are related through constraint equations of the form: Lagrange multipliers

8. 9/19/2012PHY 711 Fall 2012 -- Lecture 108 Simple example: u x y  

9. 9/19/2012PHY 711 Fall 2012 -- Lecture 109

10. 9/19/2012PHY 711 Fall 2012 -- Lecture 1010 Rational for Lagrange multipliers

11. 9/19/2012PHY 711 Fall 2012 -- Lecture 1011 Euler-Lagrange equations with constraints: Example:  r mg

12. 9/19/2012PHY 711 Fall 2012 -- Lecture 1012 Example continued:

13. 9/19/2012PHY 711 Fall 2012 -- Lecture 1013 Another example: