Conjugate points on extremal rocket paths

Existence of conjugate points on extreme rocket flight paths in trajectory optimization analysi

Research in orbit determination optimization for space trajectories

Research data covering orbit determination, optimization techniques, and trajectory design for manned space flights are summarized

The Composition of Dust in Jupiter-Family Comets as Inferred from Infrared Spectroscopy

We review the composition of Jupiter-family comet dust as inferred from infrared spectroscopy. We find that Jupiter-family comets have 10 micron silicate emission features with fluxes roughly 20-25% over the dust continuum (emission strength 1.20-1.25), similar to the weakest silicate features in Oort Cloud comets. We discuss the grain properties that change the silicate emission feature strength (composition, size, and structure/shape), and emphasize that thermal emission from the comet nucleus can have significant influence on the derived silicate emission strength. Recent evidence suggests that porosity is the dominant parameter, although more observations and models of silicates in Jupiter-family comets are needed to determine if a consistent set of grain parameters can explain their weak silicate emission features. Models of 8 m telescope and Spitzer Space Telescope observations have shown that Jupiter-family comets have crystalline silicates with abundances similar to or less than those found in Oort Cloud comets, although the crystalline silicate mineralogy of comets 9P/Tempel and C/1995 O1 (Hale-Bopp) differ from each other in Mg and Fe content. The heterogeneity of comet nuclei can also be assessed with mid-infrared spectroscopy, and we review the evidence for heterogeneous dust properties in the nucleus of comet 9P/Tempel. Models of dust formation, mixing in the solar nebula, and comet formation must be able to explain the observed range of Mg and Fe content and the heterogeneity of comet 9P/Tempel, although more work is needed in order to understand to what extent do comets 9P/Tempel and Hale-Bopp represent comets as a whole.Comment: 21 pages, 4 figures, 2 tables. Accepted for publication in Planetary and Space Scienc

On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission

Examination of accelerated first order methods for aircraft flight path optimization

Accelerated first order methods for aircraft flight path optimizatio

Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence