Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

Analytical determination of eclipse entry and exit points considering a conical shadow and oblate Earth

This paper presents a new analytical procedure to model the umbra generated during an eclipse considering an oblate ellipsoid of rotation as occulting body and a conical shadow. The method is based on purely geometrical considerations and results in the analytical definition of the entry and exit points from the conical shadow starting from the knowledge of the Sun position vector, the occulting body position vector and the orbital elements of the spacecraft orbiting the occulting body. The conical shadow also permits analytical definition of the entry and exit points of the penumbra region, which cannot be defined by using the classic cylindrical approach. Some numerical applications are proposed to test the effectiveness of the analytical formulations and to check the error in the prediction of the time spent in the shadow by the satellite. Finally, a discussion between the new conical shadow model and the classic cylindrical eclipse is carried out to see the improvements introduced by the refined geometry and the effects on space missions focusing on the cumulative error when multiple revolutions are considered

Orbital dynamics of "smart dust" devices with solar radiation pressure and drag

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris

Trajectory design and optimisation for lunar transfer

This paper deals with the design and optimization of transfer trajectories from the Earth to the Moon. In particular, the requirements of the ESMO mission have been considered. This mission, currently in its phase A, is completely designed by European students: because of this, the budget must be kept as low as possible. The mission analysis has thus to focus on low-energy transfers, in order to obtain very low cost trajectories. Two different chemical transfers are considered: a trajectory through L1 lagrangian point, considering a restricted three body problem, and a more complex Belbruno transfer, taking into account the presence of the Sun. Some results, from another low-cost lunar mission, are presented

Ground state and excitation dynamics in Ag doped helium clusters

We present a quantum Monte Carlo study of the structure and energetics of silver doped helium clusters AgHen for n up to 100. Our simulations show the first solvation shell of the Ag atom to include roughly 20 He atoms, and to possess a structured angular distribution. Moreover, the P-2(1/2)<--S-2(1/2) and P-2(3/2)<--S-2(1/2) electronic transitions of the embedded silver impurity have been studied as a function of the number of helium atoms. The computed spectra show a redshift for nless than or equal to15 and an increasing blueshift for larger clusters, a feature attributed to the effect of the second solvation shell of He atoms. For the largest cluster, the computed excitation spectrum is found in excellent agreement with the ones recorded in superfluid He clusters and bulk. No signature of the direct formation of the proposed AgHe2 exciplex is present in the computed spectrum of AgHe100. To explain the absence of the fluorescent D-2 line in the experiments, a relaxation mechanism between the P-2(3/2) and the P-2(1/2) states is proposed on the basis of the partial overlap of the excitation bands in the simulated spectra. (C) 2002 American Institute of Physics