Structure and Interpretation of Classical Mechanics
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Derive the Lagrange equations for the following systems, showing all of the intermediate steps as in the harmonic oscillator and orbital motion examples.
b. An ideal planar pendulum consists of a bob of mass connected to a pivot by a massless rod of length
subject to uniform gravitational acceleration
. A Lagrangian is
. The formal parameters of
are
,
, and
;
measures the angle of the pendulum rod to a plumb line and
is the angular velocity of the rod.
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Put ,
The Lagrange equation:
— Me@2020-09-28 05:40:42 PM
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2020.09.30 Wednesday (c) All rights reserved by ACHK