# Lagrangian Dynamics problem - need help with setup

1. Nov 17, 2005

### don_anon25

Lagrangian Dynamics problem -- need help with setup

Here's the problem:
A simple pendulum of length b and bob with mass m is attached to a massless support moving horizontally with constant acceleration a. Determine the equations of motion.

For the pendulum, x = b sin theta and y = b cos theta (Which of these equations should I use? y = b cos theta?)
For the support, x = (v0)t +.5a*t^2 - b sin theta? Is this correct?
Kinetic energy is 1/2 m (x'^2+y'^2), correct?
Potential energy is U=mgy.

If my equations are wrong, could someone tell me why and how to correct them? Your help is greatly appreciated!!!

2. Nov 17, 2005

### Physics Monkey

Remember that the support is massless so it has no kinetic or potential energy; you should just think of the support as being accelerated externally. To find the Lagrangian, you need only know the kinetic and potential energy of the pendulum, right? Start by writing the position of the pendulum relative to the support (hint: this is your usual pendulum position), and then write the position of the support relative to fixed lab (hint: this term should involve the acceleration). Once you have these two pieces, add them to obtain the position of the pendulum relative to the inertial frame. From this you can calculate the kinetic and potential energies and thus the Lagrangian.