The challenge to democracy VI. Toward a new rural statesmanship

“The people of this nation have been doing more hard thinking in the past year than ever before in our history,” declared a radio commentator in reviewing the high lights of 1940. Whether or not this sweeping assertion, which defies conclusive verification, is literally true, we may be proud and grateful that ours is one of the few countries—tragically few—in which the citizens may still think for themselves and freely express their thoughts. The evidence of that freedom is in sharp differences of public opinion and heated controversies. But with all the disagreement, there is one proposition upon which every one is agreed— the necessity for leaders to formulate our opinions into programs and to point the way to their realization. Democracy can function effectively only through organized effort, and organizations assuredly must have spokesmen. In times of so great an extension of governmental powers there is the obligation, in accord with the American way, that such exercise be not only socially effective but subject as well, at all points, to popular control. The democratic system is thus on trial as never before, and as never before there are demanded leaders of the group, of the region and of the nation as a whole

Experimental validation of phase space conduits of transition between potential wells

A phase space boundary between transition and non-transition, similar to those observed in chemical reaction dynamics, is shown experimentally in a macroscopic system. We present a validation of the phase space flux across rank one saddles connecting adjacent potential wells and confirm the underlying phase space conduits that mediate the transition. Experimental regions of transition are found to agree with the theory to within 1\%, suggesting the robustness of phase space conduits of transition in a broad array of two or more degree of freedom experimental systems, despite the presence of small dissipation.Comment: 7 pages, 6 figure

Inflation and financial market performance

An exploration of the cross-sectional relationship between inflation and an array of indicators of financial market conditions, using time-averaged data covering several decades and a large number of countries.Financial markets ; Inflation (Finance)

Constructing a Low Energy Transfer Between Jovian Moons

There has recently been considerable interest in sending a spacecraft to orbit Europa, the smallest of the four Galilean moons of Jupiter. The trajectory design involved in effecting a capture by Europa presents formidable challenges to traditional conic analysis since the regimes of motion involved depend heavily on three-body dynamics. New three-body perspectives are required to design successful and efficient missions which take full advantage of the natural dynamics. Not only does a three-body approach provide low-fuel trajectories, but it also increases the flexibility and versatility of missions. We apply this approach to design a new mission concept wherein a spacecraft "leap-frogs" between moons, orbiting each for a desired duration in a temporary capture orbit. We call this concept the "Petit Grand Tour." For this application, we apply dynamical systems techniques developed in a previous paper to design a Europa capture orbit. We show how it is possible, using a gravitional boost from Ganymede, to go from a jovicentric orbit beyond the orbit of Ganymede to a ballistic capture orbit around Europa. The main new technical result is the employment of dynamical channels in the phase space - tubes in the energy surface which naturally link the vicinity of Ganymede to the vicinity of Europa. The transfer V necessary to jump from one moon to another is less than half that required by a standard Hohmann transfer

Design of a Multi-Moon Orbiter

The Multi-Moon Orbiter concept is introduced, wherein a single spacecraft orbits several moons of Jupiter, allowing long duration observations. The ΔV requirements for this mission can be low if ballistic captures and resonant gravity assists by Jupiter’s moons are used. For example, using only 22 m/s, a spacecraft initially injected in a jovian orbit can be directed into a capture orbit around Europa, orbiting both Callisto and Ganymede enroute. The time of flight for this preliminary trajectory is four years, but may be reduced by striking a compromise between fuel and time optimization during the inter-moon transfer phases

Application of dynamical systems theory to a very low energy transfer

We use lobe dynamics in the restricted three-body problem to design orbits with prescribed itineraries with respect to the resonance regions within a Hill’s region. The application we envision is the design of a low energy trajectory to orbit three of Jupiter’s moons using the patched three-body approximation (P3BA). We introduce the “switching region,” the P3BA analogue to the “sphere of influence.” Numerical results are given for the problem of finding the fastest trajectory from an initial region of phase space (escape orbits from moon A) to a target region (orbits captured by moon B) using small controls

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the "interior" and "exterior" Hill's regions and other resonant phenomena