A Unification of Models of Tethered Satellites

In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model

A Unification of Models of Tethered Satellites

In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model

NASA Geodynamics Program

Activities and achievements for the period of May 1983 to May 1984 for the NASA geodynamics program are summarized. Abstracts of papers presented at the Conference are inlcuded. Current publications associated with the NASA Geodynamics Program are listed

UAH/NASA Workshop on Space Science Platform

The scientific user requirements for a space science platform were defined. The potential user benefits, technological implications and cost of space platforms were examined. Cost effectiveness of the platforms' capabilities were also examined

Large space structures and systems in the space station era: A bibliography with indexes

Bibliographies and abstracts are listed for 1372 reports, articles, and other documents introduced into the NASA scientific and technical information system between January 1, 1990 and June 30, 1990. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system, interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Superconducting gravity gradiometer mission. Volume 1: Study team executive summary

An executive summary is presented based upon the scientific and engineering studies and developments performed or directed by a Study Team composed of various Federal and University activities involved with the development of a three-axis Superconducting Gravity Gradiometer integrated with a six-axis superconducting accelerometer. This instrument is being developed for a future orbital mission to make precise global gravity measurements. The scientific justification and requirements for such a mission are discussed. This includes geophysics, the primary mission objective, as well as secondary objectives, such as navigation and tests of fundamental laws of physics, i.e., a null test of the inverse square law of gravitation and tests of general relativity. The instrument design and status along with mission analysis, engineering assessments, and preliminary spacecraft concepts are discussed. In addition, critical spacecraft systems and required technology advancements are examined. The mission requirements and an engineering assessment of a precursor flight test of the instrument are discussed

An iterative method for the approximation of fibers in slow-fast systems

In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers. The method is demonstrated on the Michaelis-Menten-Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in non-standard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers.Comment: To appear in SIAD

Technology for large space systems: A bibliography with indexes (supplement 16)

This bibliography lists 673 reports, articles and other documents introduced into the NASA scientific and technical information system between July 1, 1986 and December 31, 1986. Its purpose is to provide helpful information to the researcher, manager, and designer in technology development and mission design according to system interactive analysis and design, structural and thermal analysis and design, structural concepts and control systems, electronics, advanced materials, assembly concepts, propulsion, and solar power satellite systems

Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System