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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