|Sep25-07, 08:35 PM||#1|
Lagrangian and Hamiltonian Dynamics
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
Using the generalized coordinates x and y in the figure.
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 ?
|Similar Threads for: Lagrangian and Hamiltonian Dynamics|
|Lagrangian Hamiltonian||Classical Physics||0|
|Hamiltonian/Lagrangian Mechanics||Classical Physics||8|
|Hamiltonian -> Lagrangian||Advanced Physics Homework||13|
|Equivalence of Lagrangian and ADM Hamiltonian||General Physics||1|