Variable mass systems are a classic example of open systems in classical mechanics with rockets being a standard practical example. Due to the changing mass, the angular momentum of these systems is not generally conserved. Here, we show that the angular momentum vector of a free variable mass system is fixed in inertial space and, thus, is a partially conserved quantity. It is well known that such conservation rules allow simpler approaches to solving the equations of motion. This is demonstrated by using a graphical technique to obtain an analytic solution for the second Euler angle that characterizes nutation in spinning bodies.
The low-cost and short-lead time of small satellites has led to their use in science-based missions, earth observation, and interplanetary missions. Today, they are also key instruments in orchestrating technological demonstrations for on-orbit operations (O3) such as inspection and spacecraft servicing with planned roles in active debris removal and on-orbit assembly. This paper provides an overview of the robotics and autonomous systems (RASs) technologies that enable robotic O3 on smallsat platforms. Major RAS topics such as sensing & perception, guidance, navigation & control (GN&C) microgravity mobility and mobile manipulation, and autonomy are discussed from the perspective of relevant past and planned missions.
This paper examines the rotational motion of a nearly axisymmetric rocket type system with uniform burn of its propellant. The asymmetry comes from a slight difference in the transverse principal moments of inertia of the system, which then results in a set of nonlinear equations of motion even when no external torque is applied to the system. It is often difficult, or even impossible, to generate analytic solutions for such equations; closed form solutions are even more difficult to obtain. In this paper, a perturbation-based approach is employed to linearize the equations of motion and generate analytic solutions. The solutions for the variables of transverse motion are analytic and a closed-form solution to the spin rate is suggested. The solutions are presented in a compact form that permits rapid computation. The approximate solutions are then applied to the torque-free motion of a typical solid rocket system and the results are found to agree with those obtained from the numerical solution of the full non-linear equations of motion of the mass varying system.
Space telescopes are our ‘eyes in the sky’ that enable unprecedented astronomy missions and also permit Earth observation integral to science and national security. On account of the increased spatial resolution, spectral coverage, and signal-to-noise ratio, there is a constant clamour for larger aperture telescopes by the science and surveillance communities. This paper addresses a 25 m modular telescope operating in the visible wavelengths of the electromagnetic spectrum; such a telescope located at geostationary Earth orbit would permit 1 m spatial resolution of a location on Earth. Specifically, it discusses the requirements and architectural options for a robotic assembly system, called Robotic Agent for Space Telescope Assembly (RASTA). Aspects of a first-order design and initial laboratory test-bed developments are also presented.
In classical mechanics, the ‘geometry of motion’ refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterizing nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors.
Over the next two decades, unprecedented astronomy missions could be enabled by space telescopes larger than the James Webb Space Telescope. Commercially, large aperture space-based imaging systems will enable a new generation of Earth Observation missions for both science and surveillance programs. However, launching and operating such large telescopes in the extreme space environment poses practical challenges. One of the key design challenges is that very large mirrors (i.e. apertures larger than 3m) cannot be monolithically manufactured and, instead, a segmented design must be utilized to achieve primary mirror sizes of up to 100m. Even if such large primary mirrors could be made, it is impossible to stow them in the fairings of current and planned launch vehicles, e.g., SpaceX’s Starship reportedly has a 9m fairing diameter. Though deployment of a segmented telescope via a folded-wing design (as done with the James Webb Space Telescope) is one approach to overcoming this volumetric challenge, it is considered unfeasible for large apertures such as the 25m telescope considered in this study. Parallel studies conducted by NASA indicate that robotic on-orbit assembly (OOA) of these observatories offers the possibility, surprisingly, of reduced cost and risk for smaller telescopes rather than deploying them from single launch vehicles but this is not proven. Thus, OOA of large aperture astronomical and Earth Observation telescopes is of particular interest to various space agencies and commercial entities. In a new partnership with Surrey Satellite Technology Limited and Airbus Defence and Space, the Surrey Space Centre is developing the capability for autonomous robotic OOA of large aperture segmented telescopes. This paper presents the concept of operation and mission analysis for OOA of a 25m aperture telescope operating in the visible waveband of the electromagnetic spectrum; telescopes of this size will be of much value as it would permit 1m spatial resolution of a location on Earth from geostationary orbit. Further, the conceptual evaluation of robotically assembling 2m and 5m telescopes will be addressed; these missions are envisaged as essential technology demonstration precursors to the 25m imaging system.