Homework 10
1.
Problem 7.6 in the textbook. The second sentence of the problem should say, “Assume
that mass
undergoes small angular displacements…” Ignore weight in this problem.
You will need to express rotation
and the mass center displacement
of
in terms
of
and
. You should get EOMs in the form
. Are the matrices
symmetric? Next derive EOMs by using Lagrange’s equations. Derive
carefully
by imagining the virtual work done by the dashpot forces through all four virtual
displacements. Before using Lagrange’s equations, make sure that the kinetic energy is
expressed in terms of
and
rather than
and
. Now are the matrices
symmetric? Do these EOMs “agree” with the ones you derived using the Newtonian
approach? If so, how?
2.
Problem 7.1 in the textbook. Deriving these equations of motion using Newton’s second
law is very similar to what was done in the lecture notes. Next, obtain
as in the
lecture, check that
as in the lecture, and use Lagrange’s equations to derive
EOMs. Work problems 7.19, 20, 37 and 38, using MATLAB. (For vibration about
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 Spring '06
 Preston
 Energy, Mass, Velocity, Lagrange’s equations

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