Phys 3610, Fall 2008
Problem Set #5
1. Taylor,7.16
2. Taylor,7.17
3. Taylor,7.31
4. Taylor,7.34
5. Taylor,7.36
6. Taylor,7.37
f1
f2
m1
m2
7. Using the Lagrange equations, find the equations of motion for the
double pendulum, shown at the right, where the two degrees of freedom
are the two angles φ1and φ2. (The lengths of the pendulae are L1and
L2.) The two masses (m1and m2) move in a plane. Don’t assume that
the angles are small.
What you should produce are two equations (coupled) which which
are differential equations for φ1(t) and φ2(t).
Taylor does do this one in the chapter on coupled oscillators but you
should derive it for yourself, especially setting up T2, which Taylor gets
by some clever insight. Do it the usual way but get the same result!
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