The linear symmetries of Hill's lunar problem
C Aydin - Archiv der Mathematik, 2023 - Springer
Archiv der Mathematik, 2023•Springer
A symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which
leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp.
eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-
group Z 2× Z 2 and the spatial ones form the group Z 2× Z 2× Z 2. We prove that there are no
other linear symmetries. Remarkably, in Hill's system the spatial linear symmetries
determine already the planar linear symmetries.
leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp.
eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-
group Z 2× Z 2 and the spatial ones form the group Z 2× Z 2× Z 2. We prove that there are no
other linear symmetries. Remarkably, in Hill's system the spatial linear symmetries
determine already the planar linear symmetries.
Abstract
A symmetry of a Hamiltonian system is a symplectic or anti-symplectic involution which leaves the Hamiltonian invariant. For the planar and spatial Hill lunar problem, four resp. eight linear symmetries are well-known. Algebraically, the planar ones form a Klein four-group and the spatial ones form the group . We prove that there are no other linear symmetries. Remarkably, in Hill’s system the spatial linear symmetries determine already the planar linear symmetries.
Springer
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