1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lagrange's Equation with Multiple Degrees of Freedom

  1. Sep 24, 2015 #1
    Hi,

    I'm currently trying to learn about finding equations of motion from the Lagrange equation, and I'm a little confused about how it applies to multiple degree of freedom systems. I am using the following form of the equation with T as total kinetic energy, V as total potential energy, R as Rayleigh's dissipative function, ## q_i ## as the generalized coordinate, and ## Q_i ## as a generalized non-conservative force. For a MDOF system, do I have to do this equation once for each DOF?

    ## \frac{d}{dt} \left( \frac{\partial T}{\partial \dot q_{i}} \right) - \frac{\partial T}{\partial q_{i}} + \frac{\partial V}{\partial q_{i}} + \frac{\partial R}{\partial \dot q_{i}} = Q_i ##

    Thanks
     
    Last edited: Sep 24, 2015
  2. jcsd
  3. Sep 24, 2015 #2
    Yes, you will have a differential equation for each value of ##i## creating a system of differential equations.
     
  4. Sep 24, 2015 #3
    Thank you for your reply! So what is the best way to solve the resulting system of equations? Is it best to just try to use a software like MATLAB to find numerical solutions, or is there a good method for decoupling and solving the equations? If you could point me towards any good resources for this topic, that would also be very much appreciated.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lagrange's Equation with Multiple Degrees of Freedom
  1. Degrees of freedom (Replies: 6)

  2. Degrees of freedom (Replies: 4)

  3. Degrees of freedom (Replies: 2)

  4. Degrees Of Freedom (Replies: 6)

  5. Degrees of freedom (Replies: 6)

Loading...