7 citations · 18 across the 5 of their papers we have counts for
5 papers
Integrable Systems Arising from Separation of Variables on
Diana M. H. Nguyen, Sean R. Dawson, Holger R. Dullin
We show that the space of orthogonally separable coordinates on the sphere induces a natural family of integrable systems, which after symplectic reduction leads to a family…
The Harmonic Lagrange Top and the Confluent Heun Equation
Sean R. Dawson, Holger R. Dullin, Diana M. H. Nguyen
The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson str…
Monodromy in Prolate Spheroidal Harmonics
Sean R. Dawson, Holger R. Dullin, Diana M. H. Nguyen
We show that spheroidal wave functions viewed as the essential part of the joint eigenfunction of two commuting operators of has a defect in the joint spectrum that make…
The Lie-Poisson Structure of the Symmetry Reduced Regularised n-Body Problem
Suntharan Arunasalam, Holger R. Dullin, Diana M. H. Nguyen
This paper investigates the symmetry reduction of the regularised n-body problem. The three body problem, regularised through quaternions, is examined in detail. We show that for a…
The Lie-Poisson structure of the reduced n-body problem
Holger R. Dullin
The classical n-body problem in d-dimensional space is invariant under the Galilean symmetry group. We reduce by this symmetry group using the method of polynomial invariants. As a…