Closed-Form Non-Linear Sectional Analysis in the Presence of Delamination

2004 ◽  
Author(s):  
P. Guruprasad ◽  
Dineshkumar Harursampath
Keyword(s):  
Closed Form ◽  
Non Linear ◽  
Sectional Analysis

MODELING NON-LINEAR COHERENT STATES IN FIBER ARRAYS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 349-355 ◽  
Author(s):  
R. DE J. LEÓN-MONTIEL ◽  
H. MOYA-CESSA
Keyword(s):  
Closed Form ◽  
Coherent States ◽  
Bessel Functions ◽  
Displacement Operator ◽  
Fiber Arrays ◽  
Non Linear ◽  
Phase Operators

A class of nonlinear coherent states related to the Susskind-Glogower (phase) operators is obtained. We call these nonlinear coherent states as Bessel states because the coefficients that expand them into number states are Bessel functions. We give a closed form for the displacement operator that produces such states.

Closed Form Dimensional Synthesis of a High-Accuracy Four-Position Tilt Mechanism

2008 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Closed Form ◽  
Linear Equations ◽  
High Accuracy ◽  
Quadratic Equation ◽  
Optical Bench ◽  
Dimensional Synthesis ◽  
Non Linear ◽  
Stepper Motors ◽  
Synthesis Methodology ◽  
Non Linear Equations

The conceptual and closed-form dimensional synthesis of a high-accuracy four-position tilt mechanism is discussed in detail. The mechanism, which consists of a customized five-bar linkage, is capable of accurately rotating an optical bench, which supports an object such as a space instrument, or another type of similar platform to four required and discrete angular postures. The mechanism is driven by two stepper motors. Due to the special characteristics of the five-bar linkage, even relatively large stepper motor errors produce very minor errors in the four desired angular postures of the optical bench. The dimensional synthesis of the mechanism involves solving a system of four non-linear equations in four unknowns. A methodology is introduced for reducing this system of non-linear equations to a closed-form quadratic equation in one unknown. A numerical example of the closed-form dimensional synthesis methodology is also presented.

scholarly journals ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

2021 ◽  
Vol 21 (1) ◽  
pp. 145-162
Author(s):  
MERVE KARA ◽  
YASIN YAZLIK
Keyword(s):  
Closed Form ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Variable Coefficients ◽  
Linear Difference Equations ◽  
System Of Difference Equations ◽  
Solvable System ◽  
Initial Values ◽  
Non Linear ◽  
Forbidden Set

In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

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