The symplectic character of periodic orbits in the three dipole problem (Q1342441)
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scientific article; zbMATH DE number 710466
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The symplectic character of periodic orbits in the three dipole problem |
scientific article; zbMATH DE number 710466 |
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The symplectic character of periodic orbits in the three dipole problem (English)
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11 January 1995
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The authors show that in the three dipole problem only asymmetric periodic orbits exist. For these periodic orbits -- planar and three-dimensional -- of a charged particle moving under the influence of the electric field of the three dipoles they give their symplectic relations using the Hamiltonian formulation which is related to the symplectic matrix. In addition, they study the properties of the symplectic matrix and give the relations among the variations of a periodic solution, which are then used to check the accuracy of the numerical integration of equations of first order variations.
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Hamiltonian systems
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symplectic geometry
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motion of charged particles
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