Approximation of Fresnel Integrals with Applications to Diffraction Problems

Sandoval-Hernandez, M. A.; Vázquez-Leal, H.; Hernandez-Martinez, L.; Filobello-Nino, U.; Jimenez-Fernandez, Victor Manuel; Herrera-May, Agustín L.; Castaneda-Sheissa, R.; Ambrosio, Roberto; Diaz-Arango, G.

doi:10.1155/2018/4031793

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…In order to model the variability of wind pressure direction (Fig. 2), the Fresnel cosine integral was used, which can be depicted in the form [20]:…”

Section: Sample Results Of Performed Simulationsmentioning

confidence: 99%

Method of determining the effective surface area of a rigid body under wind disturbances

Cekus

Kwiatoń

2020

Arch Appl Mech

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This work proposes a method for determining the effective surface area of a rigid body induced by the wind. The proposed method assumes a variable surface effective area on which the wind acts. To determine the effective surface parameter, the dependence of normal vectors and the position change of individual vertices of the solid body were used. Cardan angles and its derivatives were used to determine the rigid body orientation in space. The free motion of the rigid body was analysed for two variants: influence of wind force and forced motion. During calculations, various cases were analysed differing in terms of wind speed and direction. A comparison of the developed method with the constant and projected surface area was presented. Various acceptable cases in which the surface area approximation is permissible were also shown. The proposed method can be used to calculate the wind load acting on a load of transport devices.

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“…In order to model the variability of wind pressure direction (Fig. 2), the Fresnel cosine integral was used, which can be depicted in the form [20]:…”

Section: Sample Results Of Performed Simulationsmentioning

confidence: 99%

Method of determining the effective surface area of a rigid body under wind disturbances

Cekus

Kwiatoń

2020

Arch Appl Mech

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“…Let ( 0 , 0 ), ( 1 , 1 ), ( 2 , 3 ), ⋯, ( , ), the coordinates of a data set, such that = 0, 1, 2, … , , and the adjustment curve is = ( , 0 , 1 , 2 , ⋯ , ), where [ 0 , 1 , … , ] are adjustment constants. The least squares approximations [30,31,32,33,34,35] attempts to minimize the sum of squares from the vertical distances of values to the ideal model ( ) and obtain the model function ( 0 , 1 , 2 , ⋯ , ), which minimizes the square error defined by:…”

Section: A Brief Introduction To the Least Squares Methodsmentioning

confidence: 99%

The novel Leal-polynomials for the multi-expansive approximation of nonlinear differential equations

Vázquez-Leal

Sandoval-Hernandez

Filobello-Nino

et al. 2020

Heliyon

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This work presents the novel Leal-polynomials (LP) for the approximation of nonlinear differential equations of different kind. The main characteristic of LPs is that they satisfy multiple expansion points and its derivatives as a mechanism to replicate behaviour of the nonlinear problem, giving more accuracy within the region of interest. Therefore, the main contribution of this work is that LP satisfies the successive derivatives in some specific points, resulting more accurate polynomials than Taylor expansion does for the same degree of their respective polynomials. Such characteristic makes of LPs a handy and powerful tool to approximate different kind of differential equations including: singular problems, initial condition and boundary-valued problems, equations with discontinuities, coupled differential equations, high-order equations, among others. Additionally, we show how the process to obtain the polynomials is straightforward and simple to implement; generating a compact, and easy to compute, expression. Even more, we present the process to approximate Gelfand's equation, an equation of an isothermal reaction, a model for chronic myelogenous leukemia, Thomas-Fermi equation, and a high order nonlinear differential equations with discontinuities getting, as result, accurate, fast and compact approximate solutions. In addition, we present the computational convergence and error studies for LPs resulting convergent polynomials and error tendency to zero as the order of LPs increases for all study cases. Finally, a study of CPU time shows that LPs require a few nano-seconds to be evaluated, which makes them suitable for intensive computing applications.

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“…As shown earlier in this section, the clothoid can be exactly represented using Fresnel integrals. The Fresnel integrals are transcendental functions that cannot be solved analytically [25]. Given that the system is intended to be used for real-time computations, ref.…”

Section: Clothoid Approximationmentioning

confidence: 99%

Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

Mbikayi,

Steinert,

Heimsch

et al. 2024

Aerospace

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The use of non-piloted eVTOL aircraft in non-segregated airspace requires reliable and deterministic automatic flight guidance systems for the aircraft to remain predictable to all the users of the airspace and maintain a high level of safety. In this paper we present a 3D trajectory generation module based on clothoid transition segments in the horizontal plane and high order polynomial transition segments in the vertical plane. The expressions of the coefficients of the polynomial are derived offline are used to generate the trajectory online, making the system capable of running in real time without requiring enormous computational power. For the horizontal plane, we focus on the flyby transition, and therefore present a thorough analysis of the flyby geometry and the limitations linked to this geometry and the construct of three-segment trajectory generation around a fixed turn rate. We present feasible solutions for these limitations, and show simulation results for the combined horizontal and vertical plane concepts, allowing the system to generate complex 3D trajectories.

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Approximation of Fresnel Integrals with Applications to Diffraction Problems

Cited by 10 publications

References 17 publications

Method of determining the effective surface area of a rigid body under wind disturbances

Method of determining the effective surface area of a rigid body under wind disturbances

The novel Leal-polynomials for the multi-expansive approximation of nonlinear differential equations

Online Deterministic 3D Trajectory Generation for Electric Vertical Take-Off and Landing Aircraft

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