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Principle of Stationary Action
A Nexus mindmap
"Lagrangian"
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"Action"
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(Sometimes called "principle of least action")
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The path that satisfies this is
the path that Nature takes
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Principle of
stationary action
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Actually, it's not a minimum!
Just require a stationary value
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It is a remarkable fact that most of
physics can be formulated as finding a
minimum of a function along a path
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Motivation
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Require that all first-order variations vanish
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A "stationary point"
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Recall the proceedure
for a function
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A "stationary trajectory"
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Essentially just a Taylor series expansion of the path
around the stationary path
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This is the general form for many variables
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An equivalent requirement are the
Euler-Lagrange
equations
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for multiple particles in 3D
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We will focus on isolated
physical systems
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The
Lagrangian
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Newton's laws
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Near surface of Earth
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e.g.
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Principle of
Stationary Action