On a Hamilton-Jacobi approach to the central orbit problem (Q2785095)
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scientific article; zbMATH DE number 1733310
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a Hamilton-Jacobi approach to the central orbit problem |
scientific article; zbMATH DE number 1733310 |
Statements
On a Hamilton-Jacobi approach to the central orbit problem (English)
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16 October 2002
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Hamilton-Jacobi approach
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central orbit
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conservation of angular momentum
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central forces
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polar angle
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Hamilton principal function
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force centre
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inverse square law
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The authors consider the problem of central forces. They point out that the angular momentum is conserved. Consequently, the time can be eliminated from the equations of motion, and so the motion may be described in terms of the polar angle rather than in terms of the time as an independent variable. Following on from this, the authors obtain a solution in terms of a Hamilton principal function with radius from force centre and polar angle as independent variables. An application of this idea to the inverse square law is given.
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