This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Lecture 10: Lagrange examples (25 Sep 09) A. DAlemberts principle, Lagrange 1. Transforming Newtons equations to eliminate forces of constraint and to reduce number of variables to n- k where k = number of constraints led to the Lagrange equations of motion ( T = kinetic energy and = potential energy): L T- d dt L q - L q = 0 , = 1 ,...,n- k 2. This transform started from F i- p i = 0, which included all forces, then calculate the work in a virtual displacement and eliminate the forces of constraint (which do no net work when summed over all the particles). 3. This was set up for a system with constraints, but could have been sim- ply a transformation to another coordinate system, such as Cartesians spherical polar coordinates. 4. The construction assumed conservative potentials F i =- i . How- ever, the important special case of the Lorentz force for charged particle in an electromagnetic field also fits into the formalism even though the...
View Full Document
This note was uploaded on 09/29/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.
- Fall '09