1. (from Marion 7-29)(adsbygoogle = window.adsbygoogle || []).push({});

A simple pendulum consist of a massmsupended by a massless spring with unextended lenghtband spring constantk.The pendulum's point of support rises vertically with constant accelerationa. 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 ?

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# Homework Help: Lagrangian and Hamiltonian Dynamics

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