4 papers
Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions
Philip Arathoon
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in ter…
Singular Reduction of the 2-Body Problem on the 3-Sphere and the 4-Dimensional Spinning Top
Philip Arathoon
We consider the dynamics and symplectic reduction of the 2-body problem on a sphere of arbitrary dimension. It suffices to consider the case for when the sphere is 3-dimensional an…
A Bijection Between the Adjoint and Coadjoint Orbits of a Semidirect Product
Philip Arathoon
We prove that there exists a geometric bijection between the sets of adjoint and coadjoint orbits of a semidirect product, provided a similar bijection holds for particular subgrou…
Hermitian flag manifolds and orbits of the Euclidean group
Philip Arathoon, James Montaldi
We study the adjoint and coadjoint representations of a class of Lie group including the Euclidean group. Despite the fact that these representations are not in general isomorphic,…