Notes
Slide Show
Outline
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Hamilton’s Principle
The motion of a given system from some initial time t1 to a later time t2 is such that the Action has a stationary value for the actual path of motion.
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Hamilton’s principle: configuration space
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Varied paths: one-dimensional extremum
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Minimum surface of revolution
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Catenary: minimum surface of revolution
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Brachistochrone Problem
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Catenary solution: brachistochrone
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Example Lagrange Multiplier: Rolling Hoop
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Example:
Lagrange Multiplier
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Coupled circuits: Lagrangian
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Change due to translation
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Change under rotation