Glossary

Every concept in the course and the lesson where it first appears. The number in brackets tells how many later lessons use it.

absolute value 0.2 Equations, inequalities, polynomials and partial fractions (2)
aircraft modes (phugoid, short period, Dutch roll) Flight dynamics 6 Longitudinal modes: the phugoid and the short period (2)
aliasing Control engineering 3.4 Digital control: sampling, the Z-transform and the controller in code
antiderivative 1.5 Integrals
atmospheric entry Astronautics 10 Atmospheric entry
attitude determination Astronautics 12 Attitude determination: sensors, TRIAD and filtering
attitude determination and control Astronautics 13 Attitude control: reaction wheels, magnetorquers and thrusters
attitude estimation Flight dynamics 3 Sensor fusion in 3D: attitude estimation with quaternions (1)
autopilot Flight dynamics 9 The autopilot: inner and outer loops (1)
average value of a function 1.5 Integrals
bang-bang control Control engineering 5.1 Pontryagin's maximum principle, time-optimal control and the shooting method
Bernoulli's equation Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces
binomial distribution 5.1 Probability and distributions
block diagram Control engineering 2.1 Block diagrams and the loop transfer function
Bode plots Control engineering 2.3 Frequency response and Bode plots (3)
boundary layer and turbulence Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces
cascade control Control engineering 3.2 Tuning: a model from a test, tuning rules and cascade control (2)
centre of mass and moment of inertia as integrals 3.3 Double and triple integrals
chain rule 1.3 Derivatives (1)
change of basis 2.2 Linear maps: rotations, change of basis, Lorentz transformation (1)
characteristic equation 4.1 Ordinary differential equations
circle 0.4 Analytic geometry and conic sections
complementary filter Control engineering 4.5 The extended Kalman filter and single-axis sensor fusion (1)
complex number 1.7 Complex numbers and phasors (8)
composition of functions 0.1 Numbers, powers, logarithms and elementary functions (1)
conic sections: ellipse, parabola, hyperbola 0.4 Analytic geometry and conic sections (3)
conservative field and potential 3.4 Line integrals, conservative fields and exact differentials (1)
continuity 1.2 Sequences, limits and continuity (1)
continuity equation 3.6 The theorems of Green, Stokes and Gauss (1)
controllability Control engineering 4.1 State feedback, pole placement and controllability
controller tuning Control engineering 3.2 Tuning: a model from a test, tuning rules and cascade control
convexity and the second derivative 1.4 Differential calculus in practice
convolution 4.3 The Fourier transform and the Dirac delta (1)
coordinate system 0.4 Analytic geometry and conic sections (1)
covariance matrix Control engineering 4.4 The Kalman filter (1)
cross product 1.1 Vectors (6)
curl 3.5 Flux, divergence and curl (2)
curvilinear unit vectors 3.2 Polar, cylindrical and spherical coordinates
cylindrical coordinates 3.2 Polar, cylindrical and spherical coordinates (1)
damped oscillator 4.1 Ordinary differential equations (2)
dead time Control engineering 1.2 How systems respond: basic elements and the step response (2)
definite integral 1.5 Integrals (10)
delay margin Control engineering 2.4 Loop stability: the −1 point, margins and delay (1)
derivative 1.3 Derivatives (6)
derivative of a vector 1.3 Derivatives (7)
determinant 2.1 Matrices, determinants and linear systems (2)
diagonalisation, principal axes 2.3 Eigenvalues and eigenvectors
differential 1.4 Differential calculus in practice (1)
differential equation, general solution 4.1 Ordinary differential equations (5)
differentiation rules 1.3 Derivatives
diffusion (heat) equation 4.7 PDEs: the wave, diffusion and Laplace equations
dimensional analysis 0.5 Units, dimensional analysis, estimation and measurement uncertainty (2)
Dirac delta 4.3 The Fourier transform and the Dirac delta (1)
direction field 4.1 Ordinary differential equations
distance between points 0.4 Analytic geometry and conic sections (1)
disturbance Control engineering 1.1 Why feedback? Open and closed loops (2)
divergence 3.5 Flux, divergence and curl (3)
divergence theorem 3.6 The theorems of Green, Stokes and Gauss (1)
dot product 1.1 Vectors (8)
double integral 3.3 Double and triple integrals (2)
eigenvalue 2.3 Eigenvalues and eigenvectors (7)
eigenvector 2.3 Eigenvalues and eigenvectors (4)
equation of a line 0.4 Analytic geometry and conic sections (1)
equilibria, stability, phase line 4.1 Ordinary differential equations (1)
Euler angles (yaw, pitch, roll) Flight dynamics 1 Attitude in 3D: rotation matrices, Euler angles, axis–angle and quaternions (1)
Euler's equations of rigid-body motion Flight dynamics 2 The rigid body in 3D: the inertia tensor, Euler's equations and the intermediate axis (4)
Euler's formula 1.7 Complex numbers and phasors (2)
Euler's method 4.1 Ordinary differential equations (2)
Euler–Lagrange equation 6.1 Calculus of variations (1)
exact and inexact differentials 3.4 Line integrals, conservative fields and exact differentials (1)
existence and uniqueness 4.1 Ordinary differential equations
exponential function 0.1 Numbers, powers, logarithms and elementary functions (5)
extended Kalman filter (EKF) Control engineering 4.5 The extended Kalman filter and single-axis sensor fusion (2)
extrema in several variables 3.1 Multivariable chain rule, extrema and Lagrange multipliers (1)
extremum of a function 1.4 Differential calculus in practice (2)
feedback Control engineering 1.1 Why feedback? Open and closed loops (2)
feedback linearisation Control engineering 4.6 Lyapunov stability and nonlinear control
feedforward Control engineering 3.3 Nonlinear reality: saturation, windup, feedforward and gain scheduling
Fermat's principle 6.1 Calculus of variations (1)
first-order lag Control engineering 1.2 How systems respond: basic elements and the step response (2)
first-order linear equation, integrating factor 4.1 Ordinary differential equations
forced oscillations and resonance 4.1 Ordinary differential equations (2)
Fourier series 4.2 Fourier series (3)
Fourier transform 4.3 The Fourier transform and the Dirac delta (1)
function 0.1 Numbers, powers, logarithms and elementary functions (3)
functional 6.1 Calculus of variations (2)
functions of several variables, level sets 1.4 Differential calculus in practice
fundamental theorem of calculus 1.5 Integrals
gain and phase margins Control engineering 2.4 Loop stability: the −1 point, margins and delay (2)
gain scheduling Control engineering 3.3 Nonlinear reality: saturation, windup, feedforward and gain scheduling (4)
Gaussian integral 3.3 Double and triple integrals (2)
geometric series 1.6 Series and power series (3)
gradient and directional derivative 1.4 Differential calculus in practice (7)
graph of a function 0.1 Numbers, powers, logarithms and elementary functions (1)
graph transformations 0.1 Numbers, powers, logarithms and elementary functions (1)
gravity assist Astronautics 8 Gravity assists
gravity turn Astronautics 4 Rocket to orbit: the rocket equation, staging and the gravity turn (1)
Green's theorem 3.6 The theorems of Green, Stokes and Gauss
ground track Astronautics 2 Orbital elements, Kepler's equation and the ground track
Hohmann transfer Astronautics 5 Orbital manoeuvres: the Hohmann transfer and plane changes (2)
hyperbolic excess speed v∞ Astronautics 7 Spheres of influence and interplanetary transfers (2)
hyperbolic functions 0.3 Trigonometry and hyperbolic functions (4)
improper integral 1.5 Integrals (4)
impulse and step response 4.4 The Laplace transform (1)
inequality 0.2 Equations, inequalities, polynomials and partial fractions (1)
inertia tensor Flight dynamics 2 The rigid body in 3D: the inertia tensor, Euler's equations and the intermediate axis (1)
initial value problem 4.1 Ordinary differential equations
integration by parts 1.5 Integrals
integration by substitution 1.5 Integrals (1)
integrator windup Control engineering 3.3 Nonlinear reality: saturation, windup, feedforward and gain scheduling (2)
inverse function 0.1 Numbers, powers, logarithms and elementary functions (2)
inverse matrix 2.1 Matrices, determinants and linear systems
inverse trigonometric functions 0.3 Trigonometry and hyperbolic functions (4)
Jacobian, change of variables 3.3 Double and triple integrals
Kalman filter Control engineering 4.4 The Kalman filter (2)
Kepler's equation Astronautics 2 Orbital elements, Kepler's equation and the ground track
Lagrange multipliers 3.1 Multivariable chain rule, extrema and Lagrange multipliers
Lambert's problem Astronautics 9 Lambert's problem and porkchop plots
Laplace transform 4.4 The Laplace transform (2)
Laplace's equation 4.7 PDEs: the wave, diffusion and Laplace equations
Laplacian 3.5 Flux, divergence and curl (2)
lateral motion Flight dynamics 7 Lateral motion: roll, spiral and Dutch roll (1)
lead–lag compensator Control engineering 2.5 Disturbances, noise and sensitivity: S, T and loop shaping
least squares 5.2 Measurement statistics and curve fitting (2)
lift, drag and aerodynamic coefficients Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces (2)
limit cycle 4.6 Nonlinear systems, phase plane and stability
limit of a function 1.2 Sequences, limits and continuity (2)
limit of a sequence 1.2 Sequences, limits and continuity (2)
line integral, work, circulation 3.4 Line integrals, conservative fields and exact differentials (2)
linear approximation 1.4 Differential calculus in practice (1)
linear function 0.1 Numbers, powers, logarithms and elementary functions (3)
linear map 2.2 Linear maps: rotations, change of basis, Lorentz transformation (1)
linear system of ODEs 4.5 Linear systems and state space
linear systems, Gaussian elimination 2.1 Matrices, determinants and linear systems (1)
linearisation about an equilibrium 4.6 Nonlinear systems, phase plane and stability (4)
lines and planes in space 1.1 Vectors (1)
logarithm 0.1 Numbers, powers, logarithms and elementary functions (8)
Lorentz transformation 2.2 Linear maps: rotations, change of basis, Lorentz transformation (1)
LQG Control engineering 5.2 LQG and robustness
LQR controller Control engineering 4.3 LQR: a cost instead of poles (4)
Lyapunov function and Lyapunov stability Control engineering 4.6 Lyapunov stability and nonlinear control
matrix and matrix operations 2.1 Matrices, determinants and linear systems (5)
matrix exponential 4.5 Linear systems and state space (2)
Maxwell's equations, integral and differential form 3.6 The theorems of Green, Stokes and Gauss (1)
mean value theorem 1.4 Differential calculus in practice
measurement noise Control engineering 1.1 Why feedback? Open and closed loops (3)
measurement uncertainty 0.5 Units, dimensional analysis, estimation and measurement uncertainty (2)
multivariable chain rule 3.1 Multivariable chain rule, extrema and Lagrange multipliers
Newton's method (root finding) 6.2 Numerical methods: Python and C++ (4)
non-minimum-phase zero Control engineering 2.2 Closed-loop poles and zeros, root locus (1)
normal distribution 5.1 Probability and distributions (3)
normal modes 2.3 Eigenvalues and eigenvectors (1)
numerical integration 1.5 Integrals (1)
Nyquist criterion Control engineering 2.4 Loop stability: the −1 point, margins and delay
observability Control engineering 4.2 State observers and observability
open loop Control engineering 1.1 Why feedback? Open and closed loops
orbit equation Astronautics 1 The two-body problem and the orbit equation (2)
orbital elements Astronautics 2 Orbital elements, Kepler's equation and the ground track (3)
orbital perturbations Astronautics 3 Perturbations: Earth's oblateness, Sun-synchronous orbits and drag
orbital plane change Astronautics 5 Orbital manoeuvres: the Hohmann transfer and plane changes
orders of magnitude and estimation 0.5 Units, dimensional analysis, estimation and measurement uncertainty
orthogonality of functions 4.2 Fourier series
overshoot Control engineering 1.2 How systems respond: basic elements and the step response (1)
partial derivative 1.4 Differential calculus in practice (10)
partial fractions 0.2 Equations, inequalities, polynomials and partial fractions (4)
passive stabilisation Astronautics 11 A spacecraft without control: spin, dual spin and gravity gradient
patched conics Astronautics 7 Spheres of influence and interplanetary transfers (1)
phase plane and classification of fixed points 4.6 Nonlinear systems, phase plane and stability (1)
phasor 1.7 Complex numbers and phasors (4)
PI controller Control engineering 1.3 P and PI control in the loop: why the integral removes the error (1)
PID controller Control engineering 3.1 The PID controller: P, I and D action and steady-state error (7)
plant Control engineering 1.1 Why feedback? Open and closed loops (1)
Poisson distribution 5.1 Probability and distributions
polar and exponential form 1.7 Complex numbers and phasors
polar coordinates 0.4 Analytic geometry and conic sections (4)
pole placement Control engineering 4.1 State feedback, pole placement and controllability (2)
polynomial 0.2 Equations, inequalities, polynomials and partial fractions (4)
Pontryagin's maximum principle Control engineering 5.1 Pontryagin's maximum principle, time-optimal control and the shooting method (1)
porkchop plot (launch windows) Astronautics 9 Lambert's problem and porkchop plots
power 0.1 Numbers, powers, logarithms and elementary functions (2)
power series, radius of convergence 1.6 Series and power series (1)
pressure, Pascal's law and buoyancy Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces
principle of least action 6.1 Calculus of variations
probability 5.1 Probability and distributions (2)
propagation of uncertainty 1.4 Differential calculus in practice (1)
quadratic equation 0.2 Equations, inequalities, polynomials and partial fractions (2)
quadratic function 0.1 Numbers, powers, logarithms and elementary functions (2)
radian measure 0.3 Trigonometry and hyperbolic functions (1)
random variable, expectation, variance 5.1 Probability and distributions (2)
real numbers 0.1 Numbers, powers, logarithms and elementary functions (1)
related rates 1.3 Derivatives
relative orbital motion Astronautics 6 Relative motion and orbital rendezvous
Reynolds number Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces
Riccati equation Control engineering 4.3 LQR: a cost instead of poles
robustness Control engineering 5.2 LQG and robustness
root 0.1 Numbers, powers, logarithms and elementary functions (1)
root locus Control engineering 2.2 Closed-loop poles and zeros, root locus (2)
roots of unity 1.7 Complex numbers and phasors
rotation matrix 2.2 Linear maps: rotations, change of basis, Lorentz transformation (2)
Routh–Hurwitz criterion Control engineering 2.2 Closed-loop poles and zeros, root locus
Runge–Kutta method 6.2 Numerical methods: Python and C++ (4)
sampling and discretisation Control engineering 3.4 Digital control: sampling, the Z-transform and the controller in code (1)
saturation Control engineering 1.3 P and PI control in the loop: why the integral removes the error (2)
scalar and vector fields 3.4 Line integrals, conservative fields and exact differentials (1)
scalar triple product 1.1 Vectors (1)
scientific notation 0.1 Numbers, powers, logarithms and elementary functions (2)
sensitivity function Control engineering 2.5 Disturbances, noise and sensitivity: S, T and loop shaping (2)
sensor fusion Control engineering 4.5 The extended Kalman filter and single-axis sensor fusion (1)
separable equation 4.1 Ordinary differential equations (1)
separation of variables, boundary conditions 4.7 PDEs: the wave, diffusion and Laplace equations (1)
sequence 1.2 Sequences, limits and continuity
series and convergence 1.6 Series and power series (1)
settling time Control engineering 1.2 How systems respond: basic elements and the step response
shooting method Control engineering 5.1 Pontryagin's maximum principle, time-optimal control and the shooting method (1)
SI units 0.5 Units, dimensional analysis, estimation and measurement uncertainty
significant figures 0.5 Units, dimensional analysis, estimation and measurement uncertainty
six-degree-of-freedom equations of motion Flight dynamics 10 Six-degree-of-freedom simulation: putting the aircraft together
sliding mode control Control engineering 4.6 Lyapunov stability and nonlinear control
spectrum 4.2 Fourier series
sphere of influence Astronautics 7 Spheres of influence and interplanetary transfers
spherical coordinates 3.2 Polar, cylindrical and spherical coordinates (5)
spherical harmonics (outline) 4.7 PDEs: the wave, diffusion and Laplace equations (1)
stability augmentation Flight dynamics 8 Stability augmentation: yaw and pitch dampers
stability derivatives Flight dynamics 5 Flight in the plane of symmetry: the longitudinal model and stability derivatives (3)
state observer (Luenberger) Control engineering 4.2 State observers and observability (1)
state space 4.5 Linear systems and state space (7)
static stability Flight dynamics 4 Static stability and trim: why an aircraft has a tail (1)
steady-state error Control engineering 1.3 P and PI control in the loop: why the integral removes the error (1)
Stirling's formula 5.1 Probability and distributions (1)
Stokes' theorem 3.6 The theorems of Green, Stokes and Gauss (2)
summation notation Σ 0.2 Equations, inequalities, polynomials and partial fractions (5)
superposition principle 4.1 Ordinary differential equations (2)
surface integral, flux 3.5 Flux, divergence and curl (3)
symplectic (leapfrog) method 6.2 Numerical methods: Python and C++
system identification Control engineering 1.2 How systems respond: basic elements and the step response (1)
system of two equations 0.2 Equations, inequalities, polynomials and partial fractions (3)
Taylor polynomial 1.4 Differential calculus in practice (4)
Taylor series 1.6 Series and power series (2)
the number e 0.1 Numbers, powers, logarithms and elementary functions (2)
thrust vector control Flight dynamics 11 The rocket: attitude and thrust vectoring (1)
time constant Control engineering 1.2 How systems respond: basic elements and the step response (1)
total differential 1.4 Differential calculus in practice (2)
trajectory tracking Flight dynamics 12 Guidance: the nominal trajectory and tracking deviations
transfer function, poles and zeros 4.4 The Laplace transform (4)
trigonometric functions 0.3 Trigonometry and hyperbolic functions (10)
trigonometric identities 0.3 Trigonometry and hyperbolic functions (2)
trim Flight dynamics 4 Static stability and trim: why an aircraft has a tail (1)
triple integral 3.3 Double and triple integrals (1)
Tsiolkovsky rocket equation Astronautics 4 Rocket to orbit: the rocket equation, staging and the gravity turn (1)
two-body problem Astronautics 1 The two-body problem and the orbit equation
type A and type B uncertainty 5.2 Measurement statistics and curve fitting
undetermined coefficients 4.1 Ordinary differential equations
unit quaternion Flight dynamics 1 Attitude in 3D: rotation matrices, Euler angles, axis–angle and quaternions (4)
unit vector 1.1 Vectors
vector 1.1 Vectors (5)
vector components 1.1 Vectors (2)
vector projection 1.1 Vectors
velocity and acceleration as derivatives 1.3 Derivatives (2)
vis-viva equation Astronautics 1 The two-body problem and the orbit equation (3)
viscosity Physics 10 Fluids: pressure, flow, viscosity and aerodynamic forces
wave equation 4.7 PDEs: the wave, diffusion and Laplace equations (1)
Z-transform Control engineering 3.4 Digital control: sampling, the Z-transform and the controller in code
Δv budget Astronautics 4 Rocket to orbit: the rocket equation, staging and the gravity turn (2)
χ² test 5.2 Measurement statistics and curve fitting