Developed Plate Expansion Using Geodesics

1984 ◽  
Vol 21 (04) ◽  
pp. 384-388
Author(s):  
John C. Clements
Keyword(s):  
Differential Equation ◽  
Numerical Quadrature ◽  
Developable Surface ◽  
Accuracy Control ◽  
Isometric Mapping ◽  
Variable Stepsize ◽  
Mapping Algorithm ◽  
Equation Solving ◽  
Expansion Procedure ◽  
The Relationship

This work is concerned with the application of a new isometric mapping algorithm to hull plate expansion procedures for ships with all or portions of the hull consisting of developable surfaces. The expansion procedure is based on the relationship between the ruling lines r⇀(s) generating the developable surface S⇀(s,t) and one additional geodesic g⇀(s) constructed within the surface as the solution of the differential equation det(g⇀'g⇀"n⇀) = 0 where n⇀ is the unit normal to S⇀ at g⇀. Precise accuracy control is achieved through the use of adaptive numerical quadrature and a variable stepsize differential equation solving routine.

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

Notes on the Riccati Equation

2005 ◽  
Vol 70 (7) ◽  
pp. 941-950 ◽  
Author(s):  
Eugene S. Kryachko
Keyword(s):  
Differential Equation ◽  
Normal Form ◽  
Riccati Equation ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Riccati Transformation ◽  
Rational Solutions ◽  
Order Polynomial ◽  
Linear Differential ◽  
The Relationship

The relationship between the Riccati and Schrödinger equations is discussed. It is shown that the transformation converting the Riccati equation into its normal form is expressed in terms of the roots of its algebraic part treated as a second-order polynomial. Together with the well-known Riccati transformation, a new transformation which also links the Riccati equation to the second-order linear differential equation is introduced. The latter is actually the Riccati transformation applied to an "inverse" Riccati equation. Two specific forms of the Riccati equation admitting the explicit particular rational solutions are obtained.

Computer simulation of the hydraulic milking method

1992 ◽  
Vol 59 (3) ◽  
pp. 253-264
Author(s):  
M. Clare Butler ◽  
Robert J. Grindal
Keyword(s):  
Differential Equation ◽  
Flow Rate ◽  
Equations Of Motion ◽  
Flow Rates ◽  
Air Inlet ◽  
Wall Movement ◽  
Linear Differential ◽  
Milking Machine ◽  
The Relationship ◽  
Return Valve

SummaryA mathematical model of the interactions within a milking machine teatcup has been developed, which describes the relationship between liner wall movement, pressures and flow rate when milking without an air inlet. It is based on equations of motion for a column of incompressible fluid and requires a second-order, non-linear differential equation to be solved. Incorporating a non-return valve allows hydraulic milking to be modelled, and the comparison between predicted and measured pressures, flow rates and liner wall movement when milking hydraulically is shown. The model can be used to optimize milking conditions to reduce vacuum peaks, improve liner opening and thus maximize flow rate.

Imbibition in a cracked porous medium

1969 ◽  
Vol 47 (22) ◽  
pp. 2519-2524 ◽  
Author(s):  
A. P. Verma
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Viscosity Ratio ◽  
Perturbation Technique ◽  
Water Imbibition ◽  
Phase Saturation ◽  
Water Viscosity ◽  
Oil Water ◽  
The Relationship ◽  
Special Case

In this paper, one special case of oil–water imbibition phenomena in a cracked porous medium of a finite length is analytically discussed. The equation for the linear countercurrent imbibition is a nonlinear differential equation whose solution has been obtained by a perturbation technique. For definiteness, specific results have been used for the relationship between relative permeability and phase saturation) impregnation function, oil–water viscosity ratio, and capillary pressure dependence on phase saturation due to Jones, Bokserman et al., Evgen'ev, and Oroveanu, respectively. An expression for the wetting phase saturation has been derived.

scholarly journals Calculation and Analysis of the Amber Interval in Traffic Flow

2019 ◽  
pp. 1-10
Author(s):  
Meng Xinyu ◽  
Zhao Jian ◽  
Zhang Wei ◽  
Meng Zhaoping
Keyword(s):  
Differential Equation ◽  
Equation Model ◽  
Related Factors ◽  
Traffic Condition ◽  
Amber Light ◽  
A Value ◽  
Differential Equation Models ◽  
Light Duration ◽  
Difficult Area ◽  
The Relationship

According to the relationship between the speed of vehicle and the amber light, we establish the differential equation model of the amber light duration. And based on the relevant conditions given in the title, three differential equation models of amber light duration under different conditions are obtained. Considering the traffic condition and driver's habit, we calculate a value that is most suitable to the actual demand. The sensitivity and stability of the model and its related factors are analyzed. We improve the model for the problem of difficult area.

Adjusting Ankle Angle Measurement Based on a Strain Gauge Bridge for Powered Transtibial Prosthesis

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Yanggang Feng ◽  
Qining Wang
Keyword(s):  
Strain Gauge ◽  
Joint Angle ◽  
Angle Measurement ◽  
Detection Accuracy ◽  
Accuracy Control ◽  
Ankle Angle ◽  
Transtibial Prosthesis ◽  
Relative Creep ◽  
Transtibial Amputees ◽  
The Relationship

Abstract Inaccurate ankle angle measurement may affect gait event detection accuracy, control parameter precision and assessment validity, and even finally result in gait asymmetry. This paper proposed an adjustment method based on a strain gauge bridge to obtain accurate ankle joint angle measurement for a powered transtibial prosthesis. The characteristics of relative creep, hysteresis, and temperature were studied. Then the curving fitting was used to study the relationship between the measured value of the strain gauge bridge and the compensation angle. Three male transtibial amputees participated in the experiments. Experimental results show that the strain gauge bridge can sense the deformation of carbon-fiber footplate, and be utilized to adjust the ankle angle. The effects of an inaccurate ankle angle were further discussed.

scholarly journals NNC: A tool based on Grammatical Evolution for data classification and differential equation solving

SoftwareX ◽  
2019 ◽  
Vol 10 ◽  
pp. 100297
Author(s):  
Ioannis G. Tsoulos ◽  
Alexandros Tzallas ◽  
Dimitris Tsalikakis
Keyword(s):  
Differential Equation ◽  
Data Classification ◽  
Grammatical Evolution ◽  
Equation Solving
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