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!

Lagrangian of 3 masses connected by springs, non-parallel.

Tags:
  1. Jul 12, 2015 #1
    Writing the Lagrangian for 3 masses and 2 springs in a line is easy.

    KE=1/2(m*v^2)

    L=KE(m1)+k/2(l1-(x2-x1))^2+KE(m2)+k2/2[L2-(x3-x2)]^2+KE(m3)

    However, I wish to model non-linear linkages of the above 3 masses and 2 springs.

    Suppose that the second spring (m2-m3) is angle θ away from the axis of the first spring (m1-m2).

    I am quite daunted by the flexing or bending of the springs.
     
  2. jcsd
  3. Jul 13, 2015 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If you simply replace the lengths by vectors, that should work. The angle will not be constant, right?
     
  4. Jul 14, 2015 #3
    @haruspex Good question about the angle being constant. The angle of intersection should be constant for a given simulation, however the springs themselves may bend.

    Using vectors sounds promising. I am not sure if the vectors (alone) would contain the necessary information given Young's modulus, which is a variation of Hook's Law that applies to the flexing that would occur given the constant angle of intersection, which I should have mentioned to begin with.

    The tricky thing about Young's modulus is that while the angles between the springs may be constant at the central mass, the relative angles between the three masses is variable due to flexing of the springs.
     
    Last edited: Jul 14, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Lagrangian of 3 masses connected by springs, non-parallel.
  1. Springs in parallel (Replies: 1)

  2. Springs in parallel? (Replies: 16)

Loading...