9/19/2012PHY 711 Fall 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

9/19/2012PHY 711 Fall Lecture 102

9/19/2012PHY 711 Fall Lecture 103

9/19/2012PHY 711 Fall Lecture 104

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

9/19/2012PHY 711 Fall Lecture 106

9/19/2012PHY 711 Fall 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

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

9/19/2012PHY 711 Fall Lecture 109

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

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

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

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