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.

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.

Scaling Evaluations on the Drag of a Hub System

2013 ◽  
Vol 58 (3) ◽  
pp. 1-13 ◽  
Author(s):  
Rajiv Shenoy ◽  
Marlin Holmes ◽  
Marilyn J. Smith ◽  
Narayanan M. Komerath
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Computational Cost ◽  
Wind Tunnel Test ◽  
Complex Model ◽  
Computational Method ◽  
Component Level ◽  
Grid Adaptation ◽  
Magnus Effect ◽  
Match Model

Parasite drag on rotorcraft can become a crucial factor in forward flight, especially during high-speed flight. Prior evaluations of the ability of computational methods to predict hub drag have focused on the ability of these solvers to match model-scale experimental data, but the results have not typically been examined for full-scale conditions. Using an unstructured computational method, the sources of hub drag on a moderately complex model are examined at different Reynolds number scales. Correlations with a 1/3.5-scale wind tunnel test and empirical data are provided to confirm the accuracy of the computations. Unlike prior efforts, grid adaptation that crosses overset mesh boundaries permits grid refinement where needed while minimizing the computational cost. For the moderately complex hub evaluated, utilization of the same grid is permissible, provided the boundary layer grid is tailored for the highest Reynolds number studied and that grid adaptation is applied. Drag evaluation illustrates that the drag of each component should be estimated at the component-level Reynolds number before consideration of the interference effects. Estimation of the interference drag for rotating hubs should additionally account for the Magnus effect, which influences the nonlinearities observed in scaling the drag and the wake.

Paper 1: Computer Solution of Surge Problems

1965 ◽  
Vol 180 (5) ◽  
pp. 62-82
Author(s):  
Victor L. Streeter
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
High Speed ◽  
Transient Flow ◽  
Nonlinear Differential Equations ◽  
Pressure Fluctuations ◽  
Transient Pressure ◽  
Pump Failure ◽  
Flow Equations ◽  
Flow Impedance

Methods for handling the transient flow equations are developed for application of the high-speed digital computer. For incompressible flow cases ordinary nonlinear differential equations occur which are solved simultaneously by established sub-routines on the computer, such as the Runge-Kutta method. For the partial differential equations of compressible water hammer with nonlinear terms such as friction, the method of characteristics and of specified time intervals are employed for those problems in which the flow changes from one steady-state to another steady-state. For steady-oscillatory flow, impedance methods have been adapted to the computer with harmonic analysis of the exciting disturbance. Experimental evidence is presented to confirm the accuracy of the procedures for single and series pipes, for pump failures, and for reciprocating pumps. Additionally the design problem of optimum operation of a valve to minimize transient pressure fluctuations has been introduced and applied to single and series pipes, including a pump failure situation.

scholarly journals Construction on the Green function for Vallee-Poussin problem for nonlinear system of differential equations

2013 ◽  
Vol 5 (1) ◽  
pp. 121-128
Author(s):  
R.I. Sobkovich ◽  
A.I. Kazmerchuk
Keyword(s):  
Green Function ◽  
Nonlinear System ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Uniqueness Theorems ◽  
System Of Differential Equations ◽  
Existence And Uniqueness Theorems ◽  
Iterative Schemes ◽  
The Green Function

Existence and uniqueness theorems of solution of n-point Vallee-Poussin problem for system of nonlinear differential equations are proved. Iterative schemes for finding them are proposed.

A Sound Derivation of the Nonlinear Differential Equations of Motion of a Travelling String

1995 ◽  
Vol 23 (3) ◽  
pp. 215-228 ◽  
Author(s):  
Patrick Bar-Avi ◽  
Itzhak Porat
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Control Volume ◽  
Direct Method ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Plane Motion ◽  
Longitudinal Vibrations ◽  
Axially Moving ◽  
Volume Method

Axially moving materials, such as high-speed magnetic tapes, belts and band saws, have been discussed since 1897. In this paper the nonlinear differential equations, which describe the string's plane motion (lateral and longitudinal), are developed by two different methods: direct method (Newton's second law) and Hamilton's principle. The control volume method is presented briefly. The equations are stated in two different coordinates systems. Comparison between the equations developed by the different methods and coordinates systems shows that they are the same. The coupling between the lateral and longitudinal vibrations is of the second order, hence linearization (to the first order) leads to uncoupled equations.

Modeling Vertical Planing Boat Motions using a Neural-Corrector Method

2021 ◽  
Author(s):  
Kyle E. Marlantes ◽  
Kevin J. Maki
Keyword(s):  
Differential Equations ◽  
High Speed ◽  
Nonlinear Differential Equations ◽  
Computational Cost ◽  
Higher Order ◽  
Operating Conditions ◽  
Irregular Waves ◽  
Linear Potential ◽  
Planing Craft ◽  
Wide Range

The dynamics of high-speed planing craft are complex and nonlinear. Standard analysis methods, such as linear potential theory, while convenient and computationally efficient, are often not suitable for use in predicting the dynamics of such craft because physical realities or design requirements invalidate the inherent assumptions. High-fidelity methods, such as state-of-the-art CFD simulations, can offer accurate solutions, but these methods are limited by computational cost and numerical sensitivity. In addition, these methods are not efficient enough to provide rapid evaluation of operability, i.e. simulations over a wide range of operating conditions and environments. This leaves few practical analysis options for small, high-speed craft designers who need to perform such predictions. In this paper, the authors present a neural-corrector method that shows promise in providing efficient predictions of vertical planing craft motions. The method retains higher-order terms typically truncated in the classical coupled 2-DOF system of ordinary differential equations using Long Short-Term Memory (LSTM) recurrent neural networks. In this manner, the robust solution provided by the linear model is retained, and the LSTM networks act as higher-order correctors. The correctors primarily regress on the solution, affording familiar numerical integration techniques for systems of nonlinear differential equations. Training and validation results from the method are compared to nonlinear simulations of 2-DOF motion of a Generic Prismatic Planing Hull (GPPH) at forward speed in head seas, with time histories given for both regular and irregular waves.

On advanced technologies of armor protection: models, materials, designs

2021 ◽  
Author(s):  
S.V. Serikov ◽  
I.K. Ustinov ◽  
A.P. Korzhavyi
Keyword(s):  
Mathematical Modeling ◽  
Differential Equations ◽  
Structural Design ◽  
Initial Velocity ◽  
High Speed ◽  
Nonlinear Differential Equations ◽  
Target Object ◽  
Vital Activity ◽  
Emergency Situations ◽  
Advanced Technologies

The creation of materials and technologies that ensure the safety of a person and objects of his vital activity in various emergency situations is impossible without modeling the properties of the main parameters of objects that pose a threat to them. Research in this direction is relevant and timely. Comprehensive studies have been carried out in terms of creating materials, structures and technologies for armor protection, analyzing and modeling the properties and parameters of the striker (object of threat) and target (object of armor protection), special attention is paid to the process of high-speed (meeting) of the striker with the target. Various options are modeled based on the properties and parameters of objects of threat and objects of armor protection with the use of modern achievements in the mechanics of destruction processes and by solving nonlinear differential equations in mathematical modeling. The prospects for the use of porous materials and structural design have been identified and shown, and methods for their preparation have been proposed. The level of survivability of the armor protection materials was modeled depending on the parameters, including the initial velocity of the objects of threat (materials, shells and bullets).

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.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

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
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