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!

Homework Help: Lagrangian and Hamiltonian Dynamics

  1. Sep 25, 2007 #1
    1. (from Marion 7-29)

    A simple pendulum consist of a mass m supended by a massless spring with unextended lenght b and spring constant k. The pendulum's point of support rises vertically with constant acceleration a. Find the Lagrange equation of motion.

    Does the motion of the mass confided in a plane? Or i need to consider the motion in 3D?
    Away from the gravitational potential energy, do i also need to consider the elastic potential energy in the spring? Is it equal to 1/2 k * b^2?

    2. (from Marion 7-33)

    Finding the Hamiltonian equation of motion of a double atwood machine
    http://thumb12.webshots.net/t/64/564/6/16/84/2610616840102234032jMZtum_th.jpg [Broken]

    Using the generalized coordinates x and y in the figure.
    i found:
    p_x = m_1 * dx/dt +m_2*(dy/dt - dx/dt) + m_3 *(dx/dt + dydt)
    p_y = m_2*(dy/dt - dx/dt) + m_3 *(dx/dt + dydt)
    H = T + U =1/2*m_1*(dx/dt)^2 + 1/2 * m_2 *(dy/dt - dx/dt)^2 + 1/2*m_3 *(dx/dt + dydt)^2 - m_1 *g*x -m_2*g*(l_1 - x +y ) - m_3*g*(l_1+l_2-x-y)

    How can i write H in terms of the generalized momentum (p_x and p_y) and coordinates only ?
    Last edited by a moderator: May 3, 2017
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted