Trim Calculation of the CH-53 Helicopter Using Numerical Continuation Method

2014 ◽  
Vol 37 (4) ◽  
pp. 1343-1349 ◽  
Author(s):  
Yihua Cao ◽  
Long Cao ◽  
Shaofeng Wan
Keyword(s):  
Continuation Method ◽  
Numerical Continuation ◽  
Trim Calculation

Numerical Solutions of Polynomial Equations for the Eight-Position Synthesis of the Cylindrical-Spherical Dyad

2012 ◽  
Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Quadratic Equation ◽  
Geometric Constraints ◽  
Numerical Continuation ◽  
Polynomial Equations ◽  
Quartic Polynomial ◽  
Solutions Of Equations ◽  
Position Synthesis

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.

scholarly journals A sticky situation

2017 ◽  
Vol 820 ◽  
pp. 1-4
Author(s):  
P.-T. Brun
Keyword(s):  
Phase Diagram ◽  
Continuation Method ◽  
Helical Structure ◽  
Numerical Continuation ◽  
Complete Phase Diagram ◽  
Observed Behaviour ◽  
Scaling Argument

The whirling helical structure obtained when pouring honey onto toast may seem like an easy enough problem to solve at breakfast. Specifically, one would hope that a quick back-of-the-envelope scaling argument would help rationalize the observed behaviour and predict the coiling frequency. Not quite: multiple forces come into play, both in the part of the flow stretched by gravity and in the coil itself, which buckles and bends like a rope. In fact, the resulting abundance of regimes requires the careful numerical continuation method reported by Ribe (J. Fluid Mech., vol. 812, 2017, R2) to build a complete phase diagram of the problem and untangle this sticky situation.

scholarly journals Numerical bifurcation and stability analysis of an predator-prey system with generalized Holling type III functional response

2018 ◽  
Vol 36 (3) ◽  
pp. 89-102
Author(s):  
Z. Lajmiri ◽  
Reza Khoshsiar Ghaziani ◽  
M. Guasemi
Keyword(s):  
Functional Response ◽  
Bifurcation Analysis ◽  
Continuation Method ◽  
Numerical Continuation ◽  
Hopf Bifurcation Point ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Bifurcation Phenomena ◽  
Stable Periodic ◽  
Numerical Bifurcation

We perform a bifurcation analysis of a predator-prey model with Holling functional response. The analysis is carried out both analytically and numerically. We use dynamical toolbox MATCONT to perform numerical bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous types of bifurcation phenomena, including fold, subcritical Hopf, cusp, Bogdanov-Takens. By starting from a Hopf bifurcation point, we approximate limit cycles which are obtained, step by step, using numerical continuation method and compute orbitally asymptotically stable periodic orbits.

scholarly journals Minimal blowing pressure allowing periodic oscillations in a simplified reed musical instrument model: Bouasse-Benade prescription assessed through numerical continuation

Acta Acustica ◽  
2020 ◽  
Vol 4 (6) ◽  
pp. 27
Author(s):  
Joel Gilbert ◽  
Sylvain Maugeais ◽  
Christophe Vergez
Keyword(s):  
Dynamical System ◽  
Continuation Method ◽  
Nonlinear Dynamical System ◽  
Period Doubling ◽  
Acoustic Resonance ◽  
Musical Instrument ◽  
Numerical Continuation ◽  
Physical Parameters ◽  
Periodic Oscillations ◽  
Nonlinear Dynamical

A reed instrument model with N acoustical modes can be described as a 2N dimensional autonomous nonlinear dynamical system. Here, a simplified model of a reed-like instrument having two quasi-harmonic resonances, represented by a four dimensional dynamical system, is studied using the continuation and bifurcation software AUTO. Bifurcation diagrams of equilibria and periodic solutions are explored with respect to the blowing mouth pressure, with focus on amplitude and frequency evolutions along the different solution branches. Equilibria and periodic regimes are connected through Hopf bifurcations, which are found to be direct or inverse depending on the physical parameters values. Emerging periodic regimes mainly supported by either the first acoustic resonance (first register) or the second acoustic resonance (second register) are successfully identified by the model. An additional periodic branch is also found to emerge from the branch of the second register through a period-doubling bifurcation. The evolution of the oscillation frequency along each branch of the periodic regimes is also predicted by the continuation method. Stability along each branch is computed as well. Some of the results are interpreted in terms of the ease of playing of the reed instrument. The effect of the inharmonicity between the first two impedance peaks is observed both when the amplitude of the first is greater than the second, as well as the inverse case. In both cases, the blowing pressure that results in periodic oscillations has a lowest value when the two resonances are harmonic, a theoretical illustration of the Bouasse-Benade prescription.

scholarly journals HARMONIC ANALYSIS OF OSCILLATORS THROUGH STANDARD NUMERICAL CONTINUATION TOOLS

2010 ◽  
Vol 20 (12) ◽  
pp. 4029-4037 ◽  
Author(s):  
FEDERICO BIZZARRI ◽  
DANIELE LINARO ◽  
BART OLDEMAN ◽  
MARCO STORACE
Keyword(s):  
Boundary Value Problem ◽  
Harmonic Analysis ◽  
Case Studies ◽  
Continuation Method ◽  
Numerical Continuation ◽  
Mechanical Oscillator ◽  
Colpitts Oscillator ◽  
Biochemical Systems ◽  
Damped Oscillator ◽  
Electronic Oscillator

In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package — without modification — such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a nonautonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.

NUMERICAL CONTINUATION FOR NONLINEAR SCHRÖDINGER EQUATIONS

2007 ◽  
Vol 17 (02) ◽  
pp. 641-656 ◽  
Author(s):  
S.-L. CHANG ◽  
C.-S. CHIEN
Keyword(s):  
Coupling Coefficient ◽  
Chemical Potential ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Lanczos Method ◽  
Iterative Refinement ◽  
Numerical Continuation ◽  
Chemical Potentials ◽  
Predictor Corrector ◽  
Centered Difference

We discuss numerical methods for studying numerical solutions of N-coupled nonlinear Schrödin-ger equations (NCNLS), N = 2, 3. First, we discretize the equations by centered difference approximations. The chemical potentials and the coupling coefficient are treated as continuation parameters. We show how the predictor–corrector continuation method can be exploited to trace solution curves and surfaces of the NCNLS, where the preconditioned Lanczos method with iterative refinement is used as the linear solver. When the chemical potential is large enough, we obtain peak solutions of the NCNLS for certain values of the coupling coefficient. The contours of the peak solutions resemble those of the experimental results of Anglin and Ketterle [2002], and Anderson et al. [1995].

Liquid rope coiling: a synoptic view

2016 ◽  
Vol 812 ◽  
Author(s):  
Neil M. Ribe
Keyword(s):  
Flow Rate ◽  
Continuation Method ◽  
Nozzle Diameter ◽  
Numerical Continuation ◽  
Critical Surface ◽  
Textile Production ◽  
Practical Applications ◽  
Contour Plots ◽  
Woven Textile ◽  
Fall Height

In liquid rope coiling, a slender jet of viscous fluid falling onto a rigid surface builds a rotating corkscrew-like structure. Here, I use a numerical continuation method to construct a complete regime diagram for liquid rope coiling. I first consider the onset of coiling, and show that a suitable onset criterion is that the radius $a_{1}$ of the rope itself be just equal to the radius $R$ of the coil. Numerical calculation of the critical surface $a_{1}=R$ in the space of the dimensionless fall height $\unicode[STIX]{x1D6F1}_{H}$, flow rate $\unicode[STIX]{x1D6F1}_{Q}$ and nozzle diameter $\unicode[STIX]{x1D6F1}_{d}$ shows that the surface has four distinct asymptotic limits corresponding to a viscous (V) mode, a gravitational (G) mode and two inertial modes (I1, I2) which are distinguished by how much the tail of the jet is stretched by gravity. Exact expressions for the onset frequencies in each of these four modes are determined. Finally, the regime diagram is constructed in the form of contour plots of the dimensionless coiling frequency as a function of $\unicode[STIX]{x1D6F1}_{H}$ and $\unicode[STIX]{x1D6F1}_{Q}$ for several values of $\unicode[STIX]{x1D6F1}_{d}$. The diagram exhibits a total of six modes: V, G, I1, I2, a multivalued inertio-gravitational (IG) mode and a third inertial mode I3 with viscosity-dominated stretching of the tail. The regime diagram permits prediction of the coiling frequency for given values of the fall height, flow rate, viscosity and nozzle diameter, and should therefore be useful in practical applications ranging from non-woven textile production to 3D printing.

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