p09fl10 - Lecture 10: Lagrange examples (25 Sep 09) A....

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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...
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This note was uploaded on 09/29/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.

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p09fl10 - Lecture 10: Lagrange examples (25 Sep 09) A....

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