Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
Claudia Maria Chanu, Luca Degiovanni, Giovanni Rastelli
TL;DR
This paper explores the application of coupling-constant metamorphosis to extended Hamiltonians, providing conditions under which integrals are preserved, with examples including the Post-Winternitz system and a 2D caged oscillator.
Contribution
It introduces conditions for preserving first integrals under coupling-constant metamorphosis in extended Hamiltonians, with practical examples.
Findings
Conditions for preserving first integrals are established.
The method is applied to the Post-Winternitz system.
The approach is demonstrated on a 2D caged oscillator.
Abstract
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm which computes the corresponding first integral of the original extended Hamiltonian. As examples, we consider the Post-Winternitz system and the 2D caged anisotropic oscillator.
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