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 Routh-Hurwitz. The methods cover the graphical approaches of the one-parameter (root locus) and two-parameter 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 second-order 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 sampled-data systems which includes the Z-transform.
The parameter estimation of linear systems is treated by a number of Data Items, featuring methods based on the least-squares 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
Section 2: Aircraft Equations of Motion
Introduction to notation for aircraft dynamics.
Notation for aircraft dynamics.
The equations of motion of a rigid aircraft.
Conversion formulae for rotation and translation of body axes.
Geometric and kinematic relationships for various axis systems.
Direction and incidence angles.
Measures of damping.
Quaternion representation of aeroplane attitude and motion characteristics.
- ESDU 67001
Section 3: Aircraft Lateral Motion
Introduction to inertia cross-coupling of the lateral and longitudinal motions during a rapid rolling manoeuvre.
Inertia cross-coupling during a rapid rolling manoeuvre. Theoretical background and discussion of simplified stability boundaries.
Inertia cross-coupling during a rapid rolling manoevre. Estimation of critical roll rate.
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
A background to the handling qualities of aircraft.
- ESDU 92006
Section 5: Aircraft Response
An introduction to rigid aeroplane response to gusts and atmospheric turbulence.
- ESDU 04024
Section 6: Aircraft Loading
Section 7: Aeroelasticity
A qualitative introduction to static aeroelasticity: controllability, loads and stability.
Static aeroelasticity: a formal analysis using assumed modes.
Static aeroelasticity: a formal analysis using normal modes.
An introduction to lateral static aeroelasticity: controllability, loads and stability.
- ESDU 96037
Section 8: Design of Linear Systems
The stability and response of linear systems. Part 1: Introduction.
The stability and response of linear systems. Part II: methods of displaying stability characteristics.
The stability and response of linear systems. Part III: methods of analysis based on frequency response.
The stability and response of linear systems. Part IV: specification and measures of system performance.
The stability and response of linear systems. Part V: control of dynamic systems.
The stability and response of linear systems. Part VI: selection of an assessment method.
The stability and response of linear systems. Part VII: examples.
- ESDU 74019
Section 9: Response of First- and Second-order Systems
Section 10: Mathematical Techniques
Solution of ordinary linear differential equations by the Laplace transform method.
A summary of the concepts relating to random processes.
Quadrature methods for the evaluation of definite integrals.
Numerical methods for the solution of ordinary differential equations: initial value problems.
- ESDU 69025
Section 11: Design of Nonlinear Systems
Section 12: Servomechanisms
Servomechanism transfer functions.
- ESDU 85026
Section 13: Sampled-data Systems
Section 14: Parameter Estimation
Parameter estimation of linear systems in the absence of process noise: (i) methods based on the least-squares principle.
Parameter estimation of linear systems in the absence of process noise: (ii) the Maximum Likelihood method.
The Kalman filter.
Parameter estimation of linear systems in the presence of process noise using the Maximum Likelihood method.
Parameter estimation of linear systems from frequency response measurements.
Parameter estimation of linear systems from frequency response measurements (computer program.)
- ESDU 87039
Users of this Series may find the following apps useful.
- Wing lift-curve slope app
A modified version of the Helmbold-Diederich equation is used to obtain the lift-curve 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 Prantl-Glauert factor, but the flow must remain both attached and wholly subcritical. The original Helmbold-Diederich equation was often used before there was general access to more soundly based methods such as the lifting-surface 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.
- Aircraft Noise
- Fatigue - Endurance Data
- Fatigue - Fracture Mechanics
- Fluid Mechanics, Internal Flow
- Fluid Mechanics, Internal Flow (Aerospace)
- Heat Transfer
- Physical Data, Chemical Engineering
- Stress and Strength
- Transonic Aerodynamics
- Vibration and Acoustic Fatigue
- Wind Engineering