PHY 711 Fall 2014 Lecture 14 1 PHY 7 11 Classical Mechanics and Mathematical Methods 101050 AM MWF Olin 103 Plan for Lecture 14 Start reading Chapter 4 Small oscillations about equilibrium ID: 474509
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PHY 711 Fall 2014 -- Lecture 14
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PHY
7
11 Classical Mechanics and Mathematical Methods
10-10:50 AM MWF Olin 103
Plan for Lecture 14:
Start reading Chapter 4
Small oscillations about equilibrium
Normal modesSlide2
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Motivation for studying small oscillations – many interacting systems have stable and meta-stable configurations which are well approximated by:Slide4
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Example – linear molecule
m
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m
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m
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Digression:Slide11
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Digression on matrices -- continued
Eigenvalues of a matrix are “invariant” under a similarity transformation Slide12
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Example of transformation:Slide13
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m
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m
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m
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m
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m
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m
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m
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m
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m
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Additional digression on matrix properties
Singular value decompositionSlide18
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Singular value decomposition -- continued