Browsing by Author "McLachlan, R."

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    Geodesics on Lie groups: Euler equations and totally geodesic subgroup
    (Massey University, 2010) Modin, K.; Perlmutter, M.; Marsland, S.; McLachlan, R.
    The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler-Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given. The setting works both in the classical nite dimensional case, and in the category of in nite dimensional Fr echet Lie groups, in which di eomorphism groups are included. Using the framework we give new examples of both nite and in nite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving di eomorphisms is totally geodesic. The paper also gives a general framework for the representation of Euler-Arnold equations in arbitrary choice of dual pairing.
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    Solution of the Young-Laplace equation for three particles
    (Massey University, 2003) Rynhart, P.R.; McLachlan, R.; Jones, J.R.; McKibbin, R.
    This paper presents the solution to the liquid bridge profile formed between three equally sized spherical primary particles. The particles are equally separated, with sphere centres located on the vertices of an equilateral triangle. Equations for the problem are derived and solved numerically for given constant mean curvature H0, contact angle , and inter-particle separation distance S. The binding force between particles is calculated and plotted as a function of liquid bridge volume for a particular example. Agreement with experiment is provided.