ESDU Dynamics Series
This Series treats the stability, response and controllability of any system that can be modelled, for some part of its motion, by linear constant coefficient differential equations.
Part of the Series is devoted solely to aircraft topics which includes the equations of motion, conversion formulae for rotation and translation of body axes, geometric and kinematic relationships for various axis systems, direction and incidence angles and measures of damping. Lateral aircraft motion covers inertia cross coupling during rapid rolling manoeuvres, including the theoretical background, a discussion of simplified stability boundaries and an estimation of the critical roll rate. Approximation to the roots of the lateral equations of motion with and without a simple yaw damper is also covered. Other topics include handling qualities, loading and aeroelasticity. The design of linear systems includes a number of Items dealing with stability, response, control and assessment. The methods start with the mathematical description of a system, including feedback, in transfer function form and system stability is assessed using RouthHurwitz. The methods cover the graphical approaches of the oneparameter (root locus) and twoparameter stability diagrams, and those based on frequency response, such as Bode and Nyquist, and the unity feedback methods of Nicholls, inverse Nyquist and Hall. Other areas covered deal with the specification and measures of system performance, the control of dynamic systems and the selection of appropriate assessment methods.
Methods for the treatment of first and secondorder systems are provided, together with a variety of methods dealing with mathematical techniques, including the Laplace transform, an introduction to random processes, quadrature and the numerical solution of differential equations. A number of other topics include the design of nonlinear systems using Describing functions, the transfer functions of a wide range of servomechanisms and the analysis of sampleddata systems which includes the Ztransform.
The parameter estimation of linear systems is treated by a number of Data Items, featuring methods based on the leastsquares principle, the Maximum Likelihood method, the Kalman filter, the Maximum Likelihood method in the presence of process noise and the parameter estimation method applied to frequency response methods.

Section 1: Organisational Documents

ESDU 00003
Dynamics Series record of documents. 
ESDU CFA
Conversion factors.

ESDU 00003

Section 2: Aircraft Equations of Motion

ESDU 67001
Introduction to notation for aircraft dynamics. 
ESDU 67002
Notation for aircraft dynamics. 
ESDU 67003
The equations of motion of a rigid aircraft. 
ESDU 67004
Conversion formulae for rotation and translation of body axes. 
ESDU 67036
Geometric and kinematic relationships for various axis systems. 
ESDU 67037
Direction and incidence angles. 
ESDU 67038
Measures of damping. 
ESDU 98024
Quaternion representation of aeroplane attitude and motion characteristics.

ESDU 67001

Section 3: Aircraft Lateral Motion

ESDU 67005
Introduction to inertia crosscoupling of the lateral and longitudinal motions during a rapid rolling manoeuvre. 
ESDU 67006
Inertia crosscoupling during a rapid rolling manoeuvre. Theoretical background and discussion of simplified stability boundaries. 
ESDU 67007
Inertia crosscoupling during a rapid rolling manoevre. Estimation of critical roll rate. 
ESDU 83024
Approximation to the roots of the lateral equations of motion of an aircraft with and without a simple yaw damper.

ESDU 67005

Section 4: Aircraft Handling Qualities

ESDU 92006
A background to the handling qualities of aircraft.

ESDU 92006

Section 5: Aircraft Response

ESDU 04024
An introduction to rigid aeroplane response to gusts and atmospheric turbulence.

ESDU 04024

Section 6: Aircraft Loading

ESDU 94009
Symmetric steady manoeuvre loads on rigid aircraft of classical configuration at subsonic speeds. 
ESDU 94045
Shear force, bending moment and torque of rigid aircraft in symmetric steady manoeuvring flight. 
ESDU 01010
Loading on a rigid aeroplane in steady lateral manoeuvres.

ESDU 94009

Section 7: Aeroelasticity

ESDU 96037
A qualitative introduction to static aeroelasticity: controllability, loads and stability. 
ESDU 97032
Static aeroelasticity: a formal analysis using assumed modes. 
ESDU 99033
Static aeroelasticity: a formal analysis using normal modes. 
ESDU 03011
An introduction to lateral static aeroelasticity: controllability, loads and stability.

ESDU 96037

Section 8: Design of Linear Systems

ESDU 74019
The stability and response of linear systems. Part 1: Introduction. 
ESDU 74020
The stability and response of linear systems. Part II: methods of displaying stability characteristics. 
ESDU 74021
The stability and response of linear systems. Part III: methods of analysis based on frequency response. 
ESDU 80002
The stability and response of linear systems. Part IV: specification and measures of system performance. 
ESDU 80018
The stability and response of linear systems. Part V: control of dynamic systems. 
ESDU 81008
The stability and response of linear systems. Part VI: selection of an assessment method. 
ESDU 81040
The stability and response of linear systems. Part VII: examples.

ESDU 74019

Section 9: Response of First and Secondorder Systems

ESDU 69005
The response of first and secondorder systems. 
ESDU 82037
The response of twodegreeoffreedom systems (computer program).

ESDU 69005

Section 10: Mathematical Techniques

ESDU 69025
Solution of ordinary linear differential equations by the Laplace transform method. 
ESDU 83041
A summary of the concepts relating to random processes. 
ESDU 85046
Quadrature methods for the evaluation of definite integrals. 
ESDU 86011
Numerical methods for the solution of ordinary differential equations: initial value problems.

ESDU 69025

Section 11: Design of Nonlinear Systems

ESDU 84009
Nonlinear systems: an introduction to Describing Functions. 
ESDU 84032
Nonlinear systems: the Describing Function method for closedloop system response.

ESDU 84009

Section 12: Servomechanisms

ESDU 85026
Servomechanism transfer functions.

ESDU 85026

Section 13: Sampleddata Systems

ESDU 86037
An introduction to the Ztransform and its application to sampleddata systems. 
ESDU 92044
Analogue to digital transformation.

ESDU 86037

Section 14: Parameter Estimation

ESDU 87039
Parameter estimation of linear systems in the absence of process noise: (i) methods based on the leastsquares principle. 
ESDU 88011
Parameter estimation of linear systems in the absence of process noise: (ii) the Maximum Likelihood method. 
ESDU 88039
The Kalman filter. 
ESDU 89032
Parameter estimation of linear systems in the presence of process noise using the Maximum Likelihood method. 
ESDU 90006
Parameter estimation of linear systems from frequency response measurements. 
ESDU 93016
Parameter estimation of linear systems from frequency response measurements (computer program.)

ESDU 87039
Users of this Series may find the following apps useful.
 Wing liftcurve slope app
A modified version of the HelmboldDiederich equation is used to obtain the liftcurve slope of a wing of trapezoidal planform, provided the wing is thin and has an aspect ratio greater than 1.5. The wing may be planar or have only moderate camber and twist. Compressibility effects are catered for by means of the classic PrantlGlauert factor, but the flow must remain both attached and wholly subcritical. The original HelmboldDiederich equation was often used before there was general access to more soundly based methods such as the liftingsurface theory that has been used as the basis of ESDU 70011. However, the modified version used in this calculator provides estimates accurate to within a few per cent of those obtained by ESDU 70011. The full background to this method, and that of ESDU 70011, is given in ESDU TM 169 in the ESDU Aerodynamics Series.
ESDU Series:
 Aerodynamics
 Aircraft Noise
 Composites
 Dynamics
 Fatigue  Endurance Data
 Fatigue  Fracture Mechanics
 Fluid Mechanics, Internal Flow
 Fluid Mechanics, Internal Flow (Aerospace)
 Heat Transfer
 Mechanisms
 Performance
 Physical Data, Chemical Engineering
 Stress and Strength
 Structures
 Transonic Aerodynamics
 Tribology
 Vibration and Acoustic Fatigue
 Wind Engineering
ESDU Packages:
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