10/22/2014phy 711 fall 2014 -- lecture 241 phy 711 classical mechanics and mathematical methods...
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10/22/2014PHY 711 Fall Lecture 243TRANSCRIPT
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PHY 711 Fall 2014 -- Lecture 24 110/22/2014
PHY 711 Classical Mechanics and Mathematical Methods
10-10:50 AM MWF Olin 103
Plan for Lecture 24:Rotational motion (Chapter 5)
1. Rigid body motion2. Moment of inertia tensor
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PHY 711 Fall 2014 -- Lecture 24 210/22/2014
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PHY 711 Fall 2014 -- Lecture 24 310/22/2014
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PHY 711 Fall 2014 -- Lecture 24 410/22/2014
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PHY 711 Fall 2014 -- Lecture 24 510/22/2014
The physics of rigid body motion; body fixed frame vs inertial frame:
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PHY 711 Fall 2014 -- Lecture 24 610/22/2014
Comparison of analysis in “inertial frame” versus “non-inertial frame”
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ˆ :Define
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system coordinate moving a ˆby Denote
system coordinate fixed a ˆby Denote
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PHY 711 Fall 2014 -- Lecture 24 710/22/2014
Properties of the frame motion (rotation):
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![Page 8: 10/22/2014PHY 711 Fall 2014 -- Lecture 241 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 24: Rotational](https://reader036.vdocuments.us/reader036/viewer/2022081517/5a4d1b507f8b9ab0599a7449/html5/thumbnails/8.jpg)
PHY 711 Fall 2014 -- Lecture 24 810/22/2014
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Effects on acceleration:
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PHY 711 Fall 2014 -- Lecture 24 910/22/2014
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![Page 10: 10/22/2014PHY 711 Fall 2014 -- Lecture 241 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 24: Rotational](https://reader036.vdocuments.us/reader036/viewer/2022081517/5a4d1b507f8b9ab0599a7449/html5/thumbnails/10.jpg)
PHY 711 Fall 2014 -- Lecture 24 1010/22/2014
ωIω
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PHY 711 Fall 2014 -- Lecture 24 1110/22/2014
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: tensorinertia ofMoment
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Example:
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PHY 711 Fall 2014 -- Lecture 24 1210/22/2014
Properties of moment of inertia tensor: Symmetric matrix real eigenvalues I1,I2,I3
orthogonal eigenvectors3,2,1 ˆˆ iI iii eeI
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: tensorinertia ofMoment
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![Page 13: 10/22/2014PHY 711 Fall 2014 -- Lecture 241 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 24: Rotational](https://reader036.vdocuments.us/reader036/viewer/2022081517/5a4d1b507f8b9ab0599a7449/html5/thumbnails/13.jpg)
PHY 711 Fall 2014 -- Lecture 24 1310/22/2014
Changing origin of rotation ''''
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PHY 711 Fall 2014 -- Lecture 24 1410/22/2014
2' 2CMjijCMiijCMjiijijij rRRrMRRRMII Rr
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and ˆˆˆ that Suppose
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![Page 15: 10/22/2014PHY 711 Fall 2014 -- Lecture 241 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 24: Rotational](https://reader036.vdocuments.us/reader036/viewer/2022081517/5a4d1b507f8b9ab0599a7449/html5/thumbnails/15.jpg)
PHY 711 Fall 2014 -- Lecture 24 1510/22/2014
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PHY 711 Fall 2014 -- Lecture 24 1610/22/2014
Descriptions of rotation about a given origin
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PHY 711 Fall 2014 -- Lecture 24 1710/22/2014
Descriptions of rotation about a given origin -- continued
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PHY 711 Fall 2014 -- Lecture 24 1810/22/2014
Descriptions of rotation about a given origin -- continued
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![Page 19: 10/22/2014PHY 711 Fall 2014 -- Lecture 241 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 24: Rotational](https://reader036.vdocuments.us/reader036/viewer/2022081517/5a4d1b507f8b9ab0599a7449/html5/thumbnails/19.jpg)
PHY 711 Fall 2014 -- Lecture 24 1910/22/2014
Descriptions of rotation about a given origin -- continued
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:equationsEuler thesolvecan we0For frame. fixedbody in thedirectly solve todifficult very is
equation torque that theNote
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PHY 711 Fall 2014 -- Lecture 24 2010/22/2014
0~~~
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:frame fixedbody in rotation for equationsEuler
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PHY 711 Fall 2014 -- Lecture 24 2110/22/2014
Solution of Euler equations for a symmetric top -- continued
)sin()(~ )cos()(~ :Solution
~ where
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PHY 711 Fall 2014 -- Lecture 24 2210/22/2014
0~~~
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:frame fixedbody in rotation for equationsEuler
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~ :Define 0~ :Suppose
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: -- topasymmetricfor Solution
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