Slow Manifold and Hannay Angle in the Spinning Top
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| Title: | Slow Manifold and Hannay Angle in the Spinning Top |
|---|---|
| Language: | English |
| Authors: | Berry, M. V., Shukla, P. |
| Source: | European Journal of Physics. Jan 2011 32(1):115-127. |
| Availability: | Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP |
| Peer Reviewed: | Y |
| Physical Description: | |
| Page Count: | 13 |
| Publication Date: | 2011 |
| Document Type: | Journal Articles Reports - Descriptive |
| Education Level: | Higher Education |
| Descriptors: | Motion, Physics, Scientific Principles, Magnets, Science Instruction, Graduate Study, College Science, Scientific Concepts, Equations (Mathematics) |
| DOI: | 10.1088/0143-0807/32/1/011 |
| ISSN: | 0143-0807 |
| Abstract: | The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at graduate-student level, of the general dynamical concept of the slow manifold. For this case, the slow manifold can be calculated exactly, and expanded as a series of reaction forces (of magnetic type) in powers of slowness, corresponding to a modified precession frequency. The forces correspond to a series for the Hannay angle for the fast motion, describing the location of a point on the top. (Contains 4 figures.) |
| Abstractor: | As Provided |
| Number of References: | 29 |
| Entry Date: | 2010 |
| Accession Number: | EJ907133 |
| Database: | ERIC |
| Abstract: | The spin of a top can be regarded as a fast variable, coupled to the motion of the axis which is slow. In pure precession, the rotation of the axis round a cone (without nutation), can be considered as the result of a reaction from the fast spin. The resulting restriction of the total state space of the top is an illustrative example, at graduate-student level, of the general dynamical concept of the slow manifold. For this case, the slow manifold can be calculated exactly, and expanded as a series of reaction forces (of magnetic type) in powers of slowness, corresponding to a modified precession frequency. The forces correspond to a series for the Hannay angle for the fast motion, describing the location of a point on the top. (Contains 4 figures.) |
|---|---|
| ISSN: | 0143-0807 |
| DOI: | 10.1088/0143-0807/32/1/011 |
