homework7 - 1 CDS 140a: Homework Set 7 Due: Wednesday,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 CDS 140a: Homework Set 7 Due: Wednesday, December 2, 2009. For the first three questions, consider the mechanical system shown in the Figure below. The mass M slides (without friction) along the curve y = x 2 . The mass m hangs by a light rod of length l (as a planar pendulum) from the mass M . Let denote the angle with the vertical, as shown. Both masses are subject to a downward gravitational force. M m y x g ; gravity y = x 2 1. Write down a Lagrangian for the system and compute the EulerLagrange equations. 2. Does this system have a conserved energy? Explain how to get this expression in both the Lagrangian and the Hamiltonian formulations of the problem. 3. Note that when M is stationary at x = 0 and m is hanging vertically (with = 0), one has an equilibrium. Is it stable? Asymptotically stable? What if one adds friction? 4. The support point of a simple planar pendulum of mass m and length l moves along the horizontal x-axis with position x ( t ) = a cos t ....
View Full Document

Page1 / 2

homework7 - 1 CDS 140a: Homework Set 7 Due: Wednesday,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online