2012 Fiscal Year Final Research Report
Application of and development in geometric mechanics
| Project/Area Number |
22540225
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
IWAI Toshihiro 京都大学, 大学院・情報学研究科, 教授 (10021635)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 力学系 / 幾何学的力学系理論 |
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| Research Abstract |
Differential geometric methods are applied to the studies of (1) the modeling of the falling cat as a port-controlled Hamiltonian system along with a realization of a somersault as an animation, (2) the reduction of the classical and quantum mechanics of a linearly deformable body by two-sided symmetry group action, (3) the parametric dependence of Chern numbers of the eigen-line bundles associated with eigenvalues of a parametric family of Hermitian matrices which are defined on the two-sphere and invariant under a discrete subgroup of the rotation group, (4) a Riemannian optimization approach to the singular value decomposition of matrices, and (5) some other projects.
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