{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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
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 θ denote the angle with the vertical, as shown. Both masses are subject to a downward gravitational force. M m y x g ; gravity θ y = x 2 1. Write down a Lagrangian for the system and compute the Euler–Lagrange 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 θ = 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 ωt .
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}