Capture Dynamics and Chaotic Motions in Celestial Mechanics
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A01=Edward Belbruno
Angular frequency
Astronomy
Author_Edward Belbruno
Ballistic capture
Barycentric coordinate system
Cantor set
Cartesian coordinate system
Category=PHD
Category=PHVB
Celestial mechanics
Center of mass (relativistic)
Chaos theory
Circular orbit
Coordinate system
Degeneracy (mathematics)
Dimension
Eccentric anomaly
Elliptic orbit
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Equations of motion
Gaussian curvature
Geometric mechanics
Halo orbit
Hamiltonian mechanics
Homoclinic orbit
Hyperbola
Hyperbolic manifold
Hyperbolic motion
Hyperbolic motion (relativity)
Hyperbolic point
Hyperbolic set
Hyperbolic trajectory
International Cometary Explorer
Invariant manifold
Inverse-square law
Invertible matrix
Kepler orbit
Kepler problem
Kepler's laws of planetary motion
Linear differential equation
Lunar distance (astronomy)
Mass distribution
Mathematical induction
Mathematical optimization
N-body problem
Orbit
Orbital elements
Orbital mechanics
Orbital plane (astronomy)
Orbital stability
Oscillation
Periodic function
Periodic point
Phase space
Planetary body
Quasiperiodic function
Quasiperiodic motion
Riemannian geometry
Rocket engine
Rotation number
Semi-major and semi-minor axes
Sitnikov problem
Spacecraft
Tangent space
Theorem
Three-body problem
Three-dimensional space (mathematics)
Transfer orbit
Transversal (geometry)
Transversality (mathematics)
Two-body problem
Two-dimensional space
Variable (mathematics)
Variational method (quantum mechanics)
Product details
- ISBN 9780691094809
- Weight: 454g
- Dimensions: 152 x 235mm
- Publication Date: 25 Jan 2004
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed.
Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.
Edward Belbruno has been a Visiting Research Collaborator in the Program in Applied and Computational Mathematics at Princeton University since 1998. The author of numerous articles in professional journals in mathematics, astronomy, and aerospace engineering, he received the Laurel Award in 1999 for the salvage of a Hughes satellite in 1998 using lunar transfer.
