Routh's sphere (Q1289582)
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scientific article; zbMATH DE number 1293234
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Routh's sphere |
scientific article; zbMATH DE number 1293234 |
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Routh's sphere (English)
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15 September 2000
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The paper gives a detailed study of the equations of motion of the Routh's sphere rolling on a horizontal plane in a constant vertical gravitational field. The derivation of first integrals is recalled, and a symmetry reduction procedure is described. The author studies the geometry of level sets of the obtained integrals, and the reduced dynamics on these level sets. Finally, using the non-Hamiltonian monodromy theorem, it is verified that the integral map of the Routh's sphere has a monodromy when the sphere becomes gyroscopically unstable.
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gyroscopic instability
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Routh's sphere
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horizontal plane
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constant vertical gravitational field
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first integrals
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symmetry reduction
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level sets
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reduced dynamics
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non-Hamiltonian monodromy theorem
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integral map
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