On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom (Q413679)
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scientific article; zbMATH DE number 6031299
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom |
scientific article; zbMATH DE number 6031299 |
Statements
On the periodic orbits of perturbed Hooke Hamiltonian systems with three degrees of freedom (English)
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7 May 2012
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Hamiltonian system
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Hooke potential
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periodic orbit
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averaging theory
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The authors study the existence of periodic solutions of a time-dependent perturbation of the Hamiltonian differential system with the Hooke potential NEWLINE\[NEWLINEH(x,y,z,p_x,p_y,p_z)=\frac12(p_x^2+p_y^2+p_z^2)+\frac12 (x^2+y^2+z^2).NEWLINE\]NEWLINE They find the expression of a first order bifurcation function and provide its complete analysis for a concrete perturbation.
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