2.032 DYNAMICS Fall 2004
Problem Set No. 2
Out: Wednesday, September 22, 2004
Due: Wednesday, September 29, 2004 at the beginning of class
Problem 1
Show that for any 3 × 3 skew-symmetric matrix A, there exists a 3-dimensional vector ω
such that for any three-dimensional vector x ,
Ax = ω × x .
Problem 2
Consider the coupled pendula shown in the figure below. Both rods are massless, with
point masses m attached to their ends. Both joints shown in the figure are frictionless. The
external force F encloses a fixed angle γ with the line of the pendulum shown. The masses
never collide. The constant of gravity is g.
Questions:
• Identify the constraints.
• Determine the number of degrees of freedom.
• Find the equations of motion for φ and ψ.
• Find the constraint forces.
• Is the system conservative? (Why?)
l1
g φ
l2
m
l3 ψ
m
F γ
Problem Set No. 2
Out: Wednesday, September 22, 2004
Due: Wednesday, September 29, 2004 at the beginning of class
Problem 1
Show that for any 3 × 3 skew-symmetric matrix A, there exists a 3-dimensional vector ω
such that for any three-dimensional vector x ,
Ax = ω × x .
Problem 2
Consider the coupled pendula shown in the figure below. Both rods are massless, with
point masses m attached to their ends. Both joints shown in the figure are frictionless. The
external force F encloses a fixed angle γ with the line of the pendulum shown. The masses
never collide. The constant of gravity is g.
Questions:
• Identify the constraints.
• Determine the number of degrees of freedom.
• Find the equations of motion for φ and ψ.
• Find the constraint forces.
• Is the system conservative? (Why?)
l1
g φ
l2
m
l3 ψ
m
F γ
