The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

L= distance between mass centers of satellites m1 and m2, tether length if m1 � m2 ,m L 0 = initial tether length, m M = total system mass, kg mi = mass of satellite i ,k g mt = tether mass, kg ri = position vector of mass mi from the system center of mass, m ˆ r1 = r1/a β, η = relative in-plane and out-of-plane swing angles between m1 and m2, respectively, deg βmax ,η max = maximum values of β and η, respectively, deg ˙ β0 = ˙ β at θ = 0 � Ha1 = maximum altitude decrease of m1 at apogee, m � Hi = altitude gain of satellite mass mi ,m � Hp2 = maximum altitude gain of m2 at perigee, m � L = decrease in the initial tether length L 0 during tether retrieval, m δ = ratio of in-plane swing rate ˙ β to the orbital rate � μ = gravitational constant, m 3 s −2 � = orbital rate, (μ/a 3 ) 1/2 , rad/s

Review on Dynamics and Control of Nonelectrodynamic Tethered Satellite Systems

Introduction M of a spacecraft presents two dynamical aspects of interest. The most obvious one is the trajectory traced by its center of mass which is governed by the classical Keplerian relations. However, spacecraft are not point masses as Kepler assumed in the analysis of planetary bodies. They have finite size and hence inertia. Thus a satellite, while negotiating a trajectory, may execute rotational motion about its center of mass, commonly referred to as libration.

Satellite attitude dynamics and control in the presence of environmental torques - A brief survey

Ever since the space tether was first proposed by Tsiolkovsky, it has been extensively utilized in space missions, for attitude stabilization, momentum exchange, and space elevators. Developments in engineering technology and changes in the space environment have diversified the current applications for the space tether. New applications for the space tether include the Tethered Space Robot, Tethered Space Net, and Tethered Spacecraft Formation. These are quickly being adapted for in-orbit maintenance such as fueling service, orbit maneuvering, and active space debris capture/removal. The flexibility and elasticity of the space tether lead to complex issues with tethered space systems, including the mechanics design, dynamics modeling and analysis, and control scheme design. In this paper, we review several new applications for the space tether during service in orbit, and research the on structure, dynamics, and control of each application. This review is conducted to provide an overall summary of the space tether for On-Orbit Servicing, and further the conversation regarding possible research interests in the future.

A review of space tether in new applications

Very low Earth orbits (VLEO), typically classified as orbits below approximately 450 km in altitude, have the potential to provide significant benefits to spacecraft over those that operate in higher altitude orbits. This paper provides a comprehensive review and analysis of these benefits to spacecraft operations in VLEO, with parametric investigation of those which apply specifically to Earth observation missions. The most significant benefit for optical imaging systems is that a reduction in orbital altitude improves spatial resolution for a similar payload specification. Alternatively mass and volume savings can be made whilst maintaining a given performance. Similarly, for radar and lidar systems, the signal-to-noise ratio can be improved. Additional benefits include improved geospatial position accuracy, improvements in communications link-budgets, and greater launch vehicle insertion capability. The collision risk with orbital debris and radiation environment can be shown to be improved in lower altitude orbits, whilst compliance with IADC guidelines for spacecraft post-mission lifetime and deorbit is also assisted. Finally, VLEO offers opportunities to exploit novel atmosphere-breathing electric propulsion systems and aerodynamic attitude and orbit control methods. 
However, key challenges associated with our understanding of the lower thermosphere, aerodynamic drag, the requirement to provide a meaningful orbital lifetime whilst minimising spacecraft mass and complexity, and atomic oxygen erosion still require further research. Given the scope for significant commercial, societal, and environmental impact which can be realised with higher performing Earth observation platforms, renewed research efforts to address the challenges associated with VLEO operations are required.

The Benefits of Very Low Earth Orbit for Earth Observation Missions

Attitude motion of a satellite subjected to gravitational and aerodynamic torques in a circular orbit is investigated. In special case, when the center of pressure of aerodynamic forces is located on one of the principal central axes of inertia of the satellite, all equilibrium orientations are determined. Necessary and (or) sufficient conditions of stability are obtained for each equilibrium orientation. Evolution of domains where stability conditions take place is investigated. All bifurcation values of parameters corresponding to qualitative change of domains of stability are determined.

Investigation of equilibria of a satellite subjected to gravitational and aerodynamic torques

Relative Equilibria of a Gyrostat Satellite with Internal Angular Momentum Along a Principal Axis

The problem of determining all equilibria of a satellite in a circular orbit is solved in the case where the satellite is subjected to gravitational and aerodynamic torques. The number of isolated equilibria is shown to be no less than eight and no more than 24. The existence proof of one-parameter families of stationary solutions is given. Using Lyapunov's method sufficient conditions for stability of isolated equilibria are obtained.

Relative equilibria of a satellite subjected to gravitational and aerodynamic torques

Device for mass measurement under zero-gravity conditions.

Dynamics of a gyrostat satellite moving along a circular orbit in a central Newtonian field of force is investigated. In a particular case, when the gyrostatic moment vector lies in one of the satellite’s principal central planes of inertia, all positions of equilibrium are determined, and the conditions of their existence are analyzed. Also determined are bifurcation values of dimensionless parameters, at which the number of equilibrium positions changes. As a result of analysis of the generalized energy integral, for each equilibrium orientation the sufficient conditions of stability are derived. Evolution of the regions where the sufficient conditions of stability are valid is investigated under variation of the system’s dimensionless parameters.

Vasily A. Sarychev

Papers

Investigation of equilibria of a satellite subjected to gravitational and aerodynamic torques

Relative Equilibria of a Gyrostat Satellite with Internal Angular Momentum Along a Principal Axis

Relative equilibria of a satellite subjected to gravitational and aerodynamic torques

Device for mass measurement under zero-gravity conditions.

Dynamics of a gyrostat satellite with the vector of gyrostatic moment in the principal plane of inertia