- Title
- Geodesics and Killing tensors in mechanics
- Creator
- Benn, I. M.
- Relation
- Journal of Mathematical Physics Vol. 47, Issue 2
- Publisher Link
- http://dx.doi.org/10.1063/1.2168121
- Publisher
- American Institute of Physics
- Resource Type
- journal article
- Date
- 2006
- Description
- Killing tensors give polynomial constants of the geodesic motion. The trajectories of a conservative mechanical system correspond to geodesics when the kinetic energy metric is conformally scaled to the Jacobi metric. Alternatively, the trajectories may be related to geodesics of some higher-dimensional warped product manifold. These two different ways of relating mechanical trajectories to geodesics are reviewed and compared. It is shown how a relation between Killing tensors on configuration space and the potential gives rise to Killing tensors on both the Jacobi and warped product manifolds.
- Subject
- Killing tensors; geodesics; mechanical trajectories
- Identifier
- http://hdl.handle.net/1959.13/926723
- Identifier
- uon:9923
- Identifier
- ISSN:1089-7658
- Language
- eng
- Reviewed
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