scholarly journals Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Error Function ◽  
Elliptic Cylinder ◽  
General Situation ◽  
3 Dimensional ◽  
Error Functions ◽  
Aerial Vehicle ◽  
Algebra Theory ◽  
In The Beginning

In this paper a new error function designed on 3-dimensional special Euclidean group SE(3) is proposed for the guidance of a UAV (Unmanned Aerial Vehicle). In the beginning, a detailed 6-DOF (Degree of Freedom) aircraft model is formulated including 12 nonlinear differential equations. Secondly the definitions of the adjoint representations are presented to establish the relationships of the Lie groups SO(3) and SE(3) and their Lie algebras so(3) and se(3). After that the general situation of the differential equations with matrices belonging to SO(3) and SE(3) is presented. According to these equations the features of the error function on SO(3) are discussed. Then an error function on SE(3) is devised which creates a new way of error functions constructing. In the simulation a trajectory tracking example is given with a target trajectory being a curve of elliptic cylinder helix. The result shows that a better tracking performance is obtained with the new devised error function.

scholarly journals The Performance of Ball during Flight Incorporate lift Force, Drag, Gravity and high Turning Velocity Trajectories Tracking Prediction

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3252-3256
Keyword(s):  
Reynolds Number ◽  
Nonlinear System ◽  
Differential Equations ◽  
High Speed ◽  
Lift Force ◽  
Nonlinear Differential Equations ◽  
3 Dimensional ◽  
Magnus Effect ◽  
Legal Guidelines ◽  
Turn Rate

—The abilities on the journey in a bag contain force, travel and gravitational. A ball with a high speed of turn has an alternate elevator and drag according to the turn rate and number of Reynolds. Furthermore, the drag power of balls is mainly distinctive as their magnitude, depth and amount imply. All the less, the golf reproductions do not reflect these differences. "This paper offers the approach to altering a track-story distance of the Golf Ball, which will be imitated by its drag depending on changes to the Reynolds Number. Similarly, because in the real world the separation from the ball from the flight can change depending on temperature, adhesiveness and height, these changes are to be observed in appropriate games. The 3 dimensional (3-D) flight of a golfing ball at taking into consideration the Magnus effect is studied inside the paper. For this purpose it is composed a gadget of six nonlinear differential equations. To decide the 3-d orientation of the ball the rotations round all three axes are given by way of the so-called Cardin angles instead of classical Euler ones. The high nonlinear system differential equations are solved numerically with the aid of a special application created in the MATLAB - Simulink surroundings. It is founded the legal guidelines of motion, velocities and accelerations on all six coordinates, as well as the projections of trajectory at the 3 coordinate planes.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Searching for optimum adsorption curve for metal sorption on soils: comparison of various isotherm models fitted by different error functions

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Péter Sipos
Keyword(s):  
Experimental Data ◽  
Error Function ◽  
Isotherm Models ◽  
Metal Sorption ◽  
Error Functions ◽  
Sorption System ◽  
Geochemical Properties ◽  
Function Combination ◽  
Soil Metal ◽  
Sorption Curve

AbstractStudies comparing numerous sorption curve models and different error functions are lacking completely for soil-metal adsorption systems. We aimed to fill this gap by studying several isotherm models and error functions on soil-metal systems with different sorption curve types. The combination of fifteen sorption curve models and seven error functions were studied for Cd, Cu, Pb, and Zn in competitive systems in four soils with different geochemical properties. Statistical calculations were carried out to compare the results of the minimizing procedures and the fit of the sorption curve models. Although different sorption models and error functions may provide some variation in fitting the models to the experimental data, these differences are mostly not significant statistically. Several sorption models showed very good performances (Brouers-Sotolongo, Sips, Hill, Langmuir-Freundlich) for varying sorption curve types in the studied soil-metal systems, and further models can be suggested for certain sorption curve types. The ERRSQ error function exhibited the lowest error distribution between the experimental data and predicted sorption curves for almost each studied cases. Consequently, their combined use could be suggested for the study of metal sorption in the studied soils. Besides testing more than one sorption isotherm model and error function combination, evaluating the shape of the sorption curve and excluding non-adsorption processes could be advised for reliable data evaluation in soil-metal sorption system.

scholarly journals Solving nonlinear differential equations with differentiable quantum circuits

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Oleksandr Kyriienko ◽  
Annie E. Paine ◽  
Vincent E. Elfving
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Quantum Circuits

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

2020 ◽  
Vol 70 (3) ◽  
pp. 599-604
Author(s):  
Şahsene Altinkaya
Keyword(s):  
Error Function ◽  
Trigonometric Polynomials ◽  
Error Functions ◽  
The Family ◽  
Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

scholarly journals Nonlinear Differential Equations Modeling the Antarctic Circumpolar Current

2021 ◽  
Vol 23 (4) ◽  
Author(s):  
Jifeng Chu ◽  
Kateryna Marynets
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Topological Degree ◽  
Antarctic Circumpolar Current ◽  
Fixed Point Theorems ◽  
Nonlinear Differential Equations ◽  
Existence Results ◽  
Circumpolar Current ◽  
The Antarctic

AbstractThe aim of this paper is to study one class of nonlinear differential equations, which model the Antarctic circumpolar current. We prove the existence results for such equations related to the geophysical relevant boundary conditions. First, based on the weighted eigenvalues and the theory of topological degree, we study the semilinear case. Secondly, the existence results for the sublinear and superlinear cases are proved by fixed point theorems.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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