Stability of the Vertical Autorotation of a Single-Winged Samara

1992 ◽  
Vol 59 (4) ◽  
pp. 1000-1008 ◽  
Author(s):  
D. Seter ◽  
A. Rosen
Keyword(s):  
Equilibrium State ◽  
Equations Of Motion ◽  
Numerical Differentiation ◽  
Aerodynamic Stability ◽  
Small Perturbations ◽  
Stability Derivatives ◽  
Basic Equilibrium ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Derivatives Of

A numerical model to investigate the stability of the vertical autorotation of a singlewinged samara is presented. This model is obtained after the method of small perturbations about an equilibrium state is applied on the nonlinear equations of motion of the samara. The aerodynamic stability derivatives of the wing are obtained by numerical differentiation. The model is used in order to study the influence of different parameters on the stability. Since the stability is highly dependent on the basic equilibrium state, the influence of the different parameters on the basic state is also presented and discussed. The theoretical model is validated by comparing its results with qualitative experimental results.

Determination of Stability Derivatives by Impulse-Response Techniques

1977 ◽  
Vol 14 (02) ◽  
pp. 265-275
Author(s):  
Carl A. Scragg
Keyword(s):  
Memory Effect ◽  
Impulse Response ◽  
Traditional Method ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Regular Motion ◽  
Stability Derivatives ◽  
The Stability ◽  
Derivatives Of

This paper presents a new method of experimentally determining the stability derivatives of a ship. Using a linearized set of the equations of motion which allows for the presence of a memory effect, the response of the ship to impulsive motions is examined. This new technique is compared with the traditional method of regular-motion tests and experimental results are presented for both methods.

Regression analysis and parameter identification

SIMULATION ◽  
1967 ◽  
Vol 9 (1) ◽  
pp. 39-47 ◽  
Author(s):  
Arthur I. Rubin ◽  
Stanley Driban ◽  
Wayne W. Miessner
Keyword(s):  
Equations Of Motion ◽  
Real Problem ◽  
Unknown Parameters ◽  
Aerodynamic Stability ◽  
Transient Time ◽  
Regression Problem ◽  
Stability Derivatives ◽  
Straight Line ◽  
Time Histories ◽  
The Stability

The steps necessary to derive the regression differential equations for a set of unknown parameters are presented. A simple straight-line algebraic regression problem is re viewed. A real problem, that of finding the aerodynamic stability derivatives for the lateral equations of motion of an airplane, is presented. Preliminary results, using real airplane transient time histories, are compared with simu lated transients obtained using wind-tunnel values for the stability derivatives.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

1973 ◽  
Vol 95 (1) ◽  
pp. 28-35 ◽  
Author(s):  
E. Harry Law ◽  
R. S. Brand
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Linear Analysis ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Nonlinear Variation ◽  
Constraint Equations ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Parametric Stability of a Two-Degree-of-Freedom Machine System: Part I—Equations of Motion and Stability

1987 ◽  
Vol 109 (2) ◽  
pp. 210-215 ◽  
Author(s):  
R. I. Zadoks ◽  
A. Midha
Keyword(s):  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Degree Of Freedom ◽  
Computationally Efficient ◽  
Machine System ◽  
Stable Operating ◽  
System Part ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Two Degree Of Freedom

An important question facing a designer is whether a certain machine system will have a stable operating condition. To date, the investigations which deal with this question have been scarce. This study treats an elastic two-degree-of-freedom system with position-dependent inertia and external forcing. In Part I, the nonlinear equations of motion are derived and linearized about the system’s steady-state rigid-body response. The stability of the linearized equations is examined using Floquet theory, and a computationally efficient method for approximating the monodromy matrix is presented. A specific example is proposed and the results are presented in Part II of this paper.

Influence of Nonlinear Wheel/Rail Contact Geometry on Stability of Rail Vehicles

1977 ◽  
Vol 99 (1) ◽  
pp. 172-185 ◽  
Author(s):  
R. Hull ◽  
N. K. Cooperrider
Keyword(s):  
Dry Friction ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Rail Vehicles ◽  
Freight Car ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Lateral Behavior ◽  
Hunting Stability

Nonlinear behavior caused by wheel flanges, worn wheel treads, and dry friction can have an important effect on rail-vehicle stability. In this paper the influence of such nonlinearities on the stability of rail freight vehicles is investigated using quasi-linearization techniques. Nonlinear equations of motion are presented that describe the lateral behavior of a 9-degree-of-freedom representation of a complete freight car with three-piece trucks. The nonlinear wheel/rail geometric constraint functions for the rolling radii, angle of wheel/rail contact, and wheelset roll angle are found by a numerical technique. The suspension description includes dry friction where appropriate. The hunting stability of the freight car is studied by employing describing-function techniques. Results are presented for a typical freight car with three different wheel profiles. The stability results illustrate the dependence of behavior on the amplitudes of vehicle motions. Application of the results in realistic situations and suggestions for future quasi-linear studies are discussed.

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