Analyzing “integral indices” to quantify the effects of a perturbing force in the harmonic and Duffing oscillators

Junior, Allan Kardec de Almeida; Prado, A. F. B. A.; Moraes, Rodolpho Vilhena de; Lara, Martı́n

doi:10.1007/s40314-017-0471-8

Cited by 7 publications

(3 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fourth type of PI is actually a variation of the third type. It was idealized in Lara (2016), and later used in de Almeida et al (2018). Since this type is the integral of the difference between the total acceleration of the disturbed particle and the acceleration of a particle in a reference orbit (a Keplerian orbit in this paper) with the same initial conditions as the disturbed one, it measures how much the disturbed orbit deviates from the reference orbit.…”

Section: Pi Methods and Perturbation Mapsmentioning

confidence: 99%

“…The concept behind the method is that the integral of the acceleration from a disturber gives the mean variation of the velocity of the spacecraft (a massless particle in the context of this paper) due to this disturber, for a given period of time T. In other words, the method measures the perturbation from a disturber, or a set of disturbers, in terms of a mean variation of the velocity of the particle. Since its first appearance (Prado 2013), the method has evolved and improved (Carvalho, de Moraes & Prado 2014;Oliveira & Prado 2014;Sanchez, Prado & Yokoyama 2014;dos Santos et al 2015;Venditti & Prado 2015;Lara 2016;de Almeida et al 2018). There are four types of integrals: the integral of the absolute value of the disturbing accelerations (type I), which is the original method; the integral of the disturbing accelerations in the direction of the velocity of the disturbed body (type II); the integral of the disturbing accelerations without the modulus (type III); and the integral of the difference between the acceleration of the disturbed body and a reference orbit (type IV).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Perturbation Maps and the ring of Haumea

Sanchez

Deienno

Prado

et al. 2020

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

ABSTRACT The dwarf planet Haumea is a trans-Neptunian object that is orbited by two moons and has a recently discovered ring. The particles of this ring are near the 3:1 resonance between the spin of Haumea and the orbital motion of the particles. In this work, the ring of Haumea is investigated using Perturbation Maps. These maps show the behaviour and impact of perturbations acting over particles around Haumea. The information coming from the maps depends on the integral type for the disturbing acceleration used to build the maps. The types II and IV are used. The numerical simulations are focused in the region between 2000 and 2500 km from the centre of Haumea, which is the region where the ring was observed, considering two initial values for the 3:1 resonant angle: θres = 0° and θres = 270°. The possible stable region for the initial angle θres = 0° is larger than the stable region for the initial angle θres = 270°. Furthermore, we found that these stable regions are not continuous, indicating that there are possible gaps in the ring. Therefore, our results suggest that Haumea may not have only one single ring, but a system of rings instead. Possible transit of the particles between the ring and the region close to the orbit of Namaka is also shown.

show abstract

Section: Pi Methods and Perturbation Mapsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Perturbation Maps and the ring of Haumea

Sanchez

Deienno

Prado

et al. 2020

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

show abstract

“…It was also applied to map orbits around asteroids 3 and to analyze the effect of the terms of the expansion of the gravity field of the Earth 1 . Other applications include the quantification of perturbative forces in harmonic and duffing oscillators and measurements of the perturbations in satellites 4 . Those ideas were later generalized, and four types of PI were described in the literature to calculate perturbation maps around asteroids 5 and to quantify the effects of the accelerations during a Powered Aero-Gravity Assisted Maneuver (PAGAM) 6 .…”

Section: Introductionmentioning

confidence: 99%

Applying the perturbative integral in aeromaneuvers around Mars to calculate the cost

Piñeros

Prado

Santos

et al. 2022

Sci Rep

View full text Add to dashboard Cite

The perturbative integral method was applied to quantify the contribution of external forces during a specific interval of time in trajectories of spacecraft around asteroids and under the Luni-solar influence. However, this method has not been used to quantify the contributions of drag in aerocapture and aerobraking. For this reason, the planet Mars is selected to apply this method during an aerogravity-assisted maneuver. Several trajectories are analyzed, making use of a drag device with area to mass ratios varying from 0.0 to 20.0 m2/kg, simulating solar sails or de-orbit devices. The mathematical model is based in the restricted three-body problem. The use of this maneuver makes it possible to obtain the variations of energy in the trajectory, replacing expensive maneuvers based on fuel consumption. To observe the effects of the maneuvers, different values of pericenter velocity and altitude were selected for prograde and retrograde orbits. The innovation of this research is the application of an integral method to quantify the delta-V of the aero gravity maneuver, comparing the cost of the maneuver with the traditional methods of space propulsion. The results allow the identification of orbits with conditions to capture, and the perturbative maps show the velocity variations.

show abstract