{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 10: Lagrange examples (25 Sep 09) A. D’Alembert’s principle, Lagrange 1. Transforming Newton’s 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 Φ = potential energy): L T - Φ d dt ∂L ˙ q σ - ∂L ∂q σ = 0 , σ = 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 Φ. 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 magnetic term has a velocity dependent force. (G. Sec 1.5, FW Sec.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern