In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
In astronautics, the Hohmann transfer orbit is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or another solar planet or asteroid. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target.
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit. While it would use little energy, transport along the network would take a long time.
Astronautics is the practice of traveling beyond Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science is its overarching field.
In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of many real-world oscillatory systems. The study of limit cycles was initiated by Henri Poincaré (1854–1912).
Janice Elaine Voss was an American engineer and a NASA astronaut. Voss received her B.S. in engineering science from Purdue University, her M.S. in electrical engineering from MIT, and her PhD in aeronautics and astronautics from MIT. She flew in space five times, jointly holding the record for American women. Voss died in Arizona on February 6, 2012, from breast cancer.
In astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers made with thruster burns to keep the active craft in the same orbit as its target. For many low Earth orbit satellites, the effects of non-Keplerian forces, i.e. the deviations of the gravitational force of the Earth from that of a homogeneous sphere, gravitational forces from Sun/Moon, solar radiation pressure and air drag, must be counteracted.
Martin Wen-Yu Lo is an American mathematician who currently works as a spacecraft trajectory expert currently working at the NASA-owned Jet Propulsion Laboratory. Martin Lo is well known for discovering the Interplanetary Superhighway, also known as the Interplanetary Transport Network. The superhighway is created by combined gravitational forces of several planets that connects planets by a network of “tunnels” and is the most efficient way to navigate the solar system. This continues to be his main area of research.
In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations.
In the mathematics of evolving systems, the concept of a center manifold was originally developed to determine stability of degenerate equilibria. Subsequently, the concept of center manifolds was realised to be fundamental to mathematical modelling.
In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor. In the case of hyperbolic dynamics, the corresponding notion is that of the hyperbolic set.
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as between the moons of Jupiter. The drawback of such trajectories is that they take longer to complete than higher-energy (more-fuel) transfers, such as Hohmann transfer orbits.
In orbital mechanics, a Lissajous orbit, named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system with minimal propulsion. Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are usually not.
A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.g., a Sun–Earth–orbiting satellite system or an Earth–Moon–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, station-keeping using thrusters may be required to keep a satellite on the orbit.
David A. Spencer is the Mars Sample Return Campaign Mission Manager at the Jet Propulsion Laboratory. As an aerospace engineer, Spencer designs and operates planetary spacecraft.
Malcolm D. Shuster was an American physicist and aerospace engineer, whose work contributed significantly to spacecraft attitude determination. In 1977 he joined the Attitude Systems Operation of the Computer Sciences Corporation in Silver Spring, Maryland, during which time he developed the QUaternion ESTimator (QUEST) algorithm for static attitude determination. He later, with F. Landis Markley, helped to develop the standard implementation of the Kalman filter used in spacecraft attitude estimation. During his career, he authored roughly fifty technical papers on subjects in physics and spacecraft engineering, many of which have become seminal within the field of attitude estimation, and held teaching assignments at Johns Hopkins University, Howard University, Carnegie-Mellon University and Tel-Aviv University. In 2000 the American Astronautical Society awarded him the Dirk Brouwer Award. In June 2005 the American Astronautical Society held a special three-day Astronautics symposium in his honor
Daniele Mortari is Professor of Aerospace Engineering at Texas A&M University and Chief Scientist for Space for Texas A&M ASTRO Center. Mortari is known for inventing the Flower Constellations and the k-vector range searching technique and the Theory of Functional Connections.
James Michael Longuski is an American scientist, inventor, writer, and educator known for his contributions to astrodynamics and space mission design. After working as a space mission designer at Jet Propulsion Laboratory (JPL) for NASA, Longuski has served as a professor at Purdue University School of Aeronautics and Astronautics since 1988.
Maruthi Ram Akella is an Indian-American aerospace engineer. Akella specializes in the control of complex dynamical systems that are subject to large scale nonlinearities and uncertainties.
