On algebraic integrals of the motion of a point over a quadric in a quadratic potential (Q5938490)
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scientific article; zbMATH DE number 1622462
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On algebraic integrals of the motion of a point over a quadric in a quadratic potential |
scientific article; zbMATH DE number 1622462 |
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On algebraic integrals of the motion of a point over a quadric in a quadratic potential (English)
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22 July 2001
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The author considers the following problem. Let a point move on a quadric \(a_1 x_1^2 + \dots + a_n x_n^2 = 1\) in a potential field with potential of the form \(V(x) = c_1 x_1^2 + \dots + c_n x_n^2\). When there exists a complete family of \(n-1\) involutive first integrals which are algebraic in coordinates and momenta? The author proves that this is possible only in some special cases which were found by Jacobi and Neumann.
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Hamiltonian system
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algebraic first integral
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quadratic potential
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Jacobi integral
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Neumann integral
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