Download Dynamical Systems, the Three-Body Problem and Space Mission by Wang Sang Koon, Martin W Lo, University Jerrold E Marsden, PDF

By Wang Sang Koon, Martin W Lo, University Jerrold E Marsden, Shane D Ross

Explores low-energy passageways in area that can minimize the volume of gas spacecraft have to discover and advance our sun method. This publication develops instruments for the layout of trajectories that take complete benefit of ordinary 3 or extra physique dynamics, thereby saving necessary gas and gaining flexibility in undertaking making plans.

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Extra info for Dynamical Systems, the Three-Body Problem and Space Mission Design (Interdisciplinary Applied Mathematics)

Example text

Furthermore, for a fixed energy E, consider a neighborhood of L in the energy surface, whose position space projections are the neck regions described previously. We refer to this neighborhood as the equilibrium region and denote it by R on the energy surface. Following our adopted convention, R has the position space projection R. Hamiltonian Approach. 11) as expanded about (xe , ye , pxe , pye ) = (xe , 0, 0, xe ). After making a coordinate change with (xe , 0, 0, xe ) as the origin, these quadratic terms form the Hamiltonian function for the linearized equations, which we shall call Hl .

This theorem can also be taken as a proof of “horseshoe-like” chaos in the system. 20 1. Introduction In Chapter 4, we use the tubes and their intersections to compute orbits of desired itineraries with respect to the aforementioned realms of the phase space and make the connection to the design of space mission trajectories. In Chapter 5, we construct solutions of the restricted four-body problem using solutions of the restricted three-body problem as building blocks. This approach, which is appropriate for some low energy space mission trajectories, is the patched three-body approximation.

These curves bound the zone, in white, accessible by the particle, P , for a given energy value, E = e. The part of the x-y plane which is shaded is inaccessible for a given energy, and known as the forbidden realm. The outermost accessible realm, known as the exterior realm, extends to infinity. In the fifth case (e), the forbidden realm vanishes and motion over the entire x-y plane is possible. Contour plots of the effective potential give the five cases of Hill’s region. 2 are the Hill’s region and the shaded areas are the forbidden realm.

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