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This course is intended to give the students familiarity with the dynamics of rotational motion, as a concrete example of tensors, eigenvalues and normal modes of motion.
The conceptual center is the discovery and use of normal modes of motion arising in the diagonalization of a quadratic form. The students will already have seen this procedure in the treatment of coupled oscillators (paradigm 7), but here we have a different topology. Cyclic coordinates take on their literal meaning.
The students will gain skills and insights into the process of choosing and changing coordinate systems. They will develop familiarity with the center of-mass system. Math skills will be developed around the concrete example of the inertial tensor, which allows visualization of the meaning of eigenvectors as well as eigenvalues.
A final topic is how motion is modified by external factors. Students will observe the gravitational precession of a weighted gyroscope, which illustrates both the effect of a constraint and the effect of a symmetry breaking force (gravity). They will then have a brief introduction to Larmor precession in both classical and quantum mechanics, returning to the NMR lab as a finale.
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Last Update 9/24/09, webpage created by Corinne Manogue,
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