Search

Performing orbital insertion around Mars using aerocapture instead of a propulsive orbit insertion manoeuvre allows to save resources and/or increase the payload mass fraction. Aerocapture has never been employed to date because of the high uncertainties in the parameters from which it depends, mainly related to atmospheric density modeling and navigation errors. The purpose of this work is to investigate the feasibility of aerocapture at Mars with an innovative deployable drag device, whose aperture can be modulated in flight, and assess the effects of the main uncertainties on the success of the manoeuvre. This paper starts with the presentation of a parametric bi-dimensional analysis of the effectiveness of aerocapture, for which a wide range of uncertainty levels in the atmospheric density and the ballistic coefficient are considered. Then, an application to a real mission scenario is carried out including the error of the targeting manoeuvre performed at the limit of the sphere of influence of the planet. The analyses show the strong influence of the uncertainties in the atmospheric density and the ballistic coefficient, which significantly narrow the solution space and limit its continuity. However, viable solutions for aerocapture can still be identified even in the worst conditions.

We prove that one can obtain natural bundles of Lie algebras on rank two s-K\"ahler manifolds, whose fibres are isomorphic to so(s+1,s+1), su(s+1,s+1) and sl(2s + 2,\R). In the most rigid case (which includes complex tori and abelian varieties) these bundles have natural flat connections, whose flat global sections act naturally on cohomology. We also present several natural examples of manifolds which can be equipped with an s-K\"ahler structure with various levels of rigidity: complex tori and abelian varieties, cotangent bundles of smooth manifolds and moduli of pointed elliptic curves., Comment: in v2 a new theorem in Section 8 has been added

We determine the structure of the $*$-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ with the full special linear superalgebras of some graded vector spaces isotypical with respect to a natural action of $\mathbf{so}(3,\R)$. We provide an explicit description of one of the real forms of this superalgebra, which is geometrically natural being made of $\mathbf{so}(3,\R)$-invariant operators which preserve the Poincar\'e (odd Hermitean) inner product on the bundle of forms., Comment: 20 pages, 4 tables. Minor changes in presentation from v1

Given an orientable weakly self-dual manifold X of rank two, we build a geometric realization of the Lie algebra sl(6,C) as a naturally defined algebra L of endomorphisms of the space of differential forms of X. We provide an explicit description of Serre generators in terms of natural generators of L. This construction gives a bundle on X which is related to the search for a natural Gauge theory on X. We consider this paper as a first step in the study of a rich and interesting algebraic structure., Comment: 16 pages, no figures

For all $m > 0$ we build a two-dimensional family of smooth manifolds of real dimension $3m + 2$ and use it to interpolate between the anticanonical family in the complex projective space of dimension $m + 1$ and its mirror dual. The main tool is the notion of self-dual manifold., Comment: 21 pages, no figures; in v2 corrected typo in Definition 2.1

We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the existence of a transformation similar to the Fourier-Mukai functor, suggest that this approach may be able to explain mirror symmetry also in other situations, Comment: 22 pages

In the first part of this paper we begin the study of polysymplectic manifolds, and of their relationship with PDE's. This notion provides a generalization of symplectic manifolds which is very well suited for the geometric study of PDE's with values in a smooth manifold. Some of the standard tools of analytical mechanics, such as the Legendre transformation and Hamilton's equations, are shown to generalize to this new setting. There is a strong link with lagrangian fibrations, which can be used to build polysymplectic manifolds. We then provide the definition and some basic properties of s-Kahler and almost s-Kahler manifolds. These are a generalization of the usual notion of Kahler and almost Kahler manifold, and they reduce to them for s=1. The basic properties of Kahler manifolds, and their Hodge theory, can be generalized to s-Kahler manifolds, with some modifications. The most interesting examples come from semi-flat special lagrangian fibrations of Calabi-Yau manifolds., Comment: 56 pages, LaTeX2e, no figures