Noesis

Physics

Motion, fields, waves and the laws that bind them.

notes
536notes
chapters
19chapters
tests
98tests
words
1.1Mwords
Test bank →Learning path →Deep dives → (536 topics)

Phase 1 — Foundation Physics

4–6 months @ 2 hrs/day · Begin after Math Phase 1–28 chapters
1.1

Measurement, Vectors & Kinematics

22 topics
  1. 1.1.1Physical quantities — fundamental and derived
  2. 1.1.2SI units — seven base units and all derived units
  3. 1.1.3Dimensional analysis — checking equations, deriving relations
  4. 1.1.4Significant figures — rules for operations
  5. 1.1.5Errors — absolute, relative, percentage; systematic vs random
  6. 1.1.6Scalars vs vectors — definition, examples
  7. 1.1.7Vector representation — magnitude, direction, components
  8. 1.1.8Vector addition — triangle law, parallelogram law
  9. 1.1.9Resolution of vectors — into components (any axes)
  10. 1.1.10Unit vectors — î, ĵ, k̂; constructing unit vector
  11. 1.1.11Dot product — formula, geometric meaning, work calculation
  12. 1.1.12Cross product — formula, direction (right-hand rule), torque - area calculation
  13. 1.1.13Position vector, displacement, distance
  14. 1.1.14Average velocity vs instantaneous velocity
  15. 1.1.15Average acceleration vs instantaneous acceleration
  16. 1.1.16Equations of motion (SUVAT) — derivations from calculus
  17. 1.1.17Free fall — g = 9.8 m - s², sign conventions
  18. 1.1.18Graphs — x-t, v-t, a-t; areas and slopes meaning
  19. 1.1.19Projectile motion — horizontal - vertical independence, full derivation
  20. 1.1.20Range, max height, time of flight — all derived
  21. 1.1.21Relative motion — 1D and 2D; river-boat problems
  22. 1.1.22Reference frames — Galilean transformations
1.2

Newton's Laws & Dynamics

25 topics
  1. 1.2.1Newton's first law — inertia, operational definition of force
  2. 1.2.2Newton's second law — F = ma (net force), impulse-momentum form
  3. 1.2.3Newton's third law — action-reaction, common misconceptions
  4. 1.2.4Free body diagrams — systematic drawing technique
  5. 1.2.5Normal force — reaction force, not always = mg
  6. 1.2.6Friction — static (maximum), kinetic, rolling
  7. 1.2.7Coefficients of friction — measurement, material dependence
  8. 1.2.8Angle of friction, angle of repose — derivation
  9. 1.2.9Tension in inextensible strings
  10. 1.2.10Atwood machine — derivation
  11. 1.2.11Inclined planes — with and without friction
  12. 1.2.12Pulley systems — mechanical advantage
  13. 1.2.13Non-inertial reference frames — pseudo forces
  14. 1.2.14Rotating frames — centrifugal force, Coriolis force
  15. 1.2.15Circular motion — centripetal acceleration derivation
  16. 1.2.16Centripetal force — what provides it in various situations
  17. 1.2.17Banking of roads — derivation
  18. 1.2.18Vertical circular motion — minimum speed conditions
  19. 1.2.19Newton's law of gravitation — universal, action at distance
  20. 1.2.20Gravitational field intensity g = GM - r²
  21. 1.2.21Variation of g — with altitude, latitude, depth
  22. 1.2.22Gravitational potential energy — U = −GMm - r (not mgh)
  23. 1.2.23Escape velocity — derivation
  24. 1.2.24Orbital velocity for circular orbit — derivation
  25. 1.2.25Weightlessness — true (free fall) vs apparent
1.3

Work, Energy & Power

13 topics
  1. 1.3.1Work — definition, dot product F·d, sign convention
  2. 1.3.2Work done by variable force — integration
  3. 1.3.3Work-energy theorem — derivation from Newton's second law
  4. 1.3.4Kinetic energy — derivation
  5. 1.3.5Potential energy — definition, gravitational (mgh and −GMm - r), elastic (½kx²)
  6. 1.3.6Conservative forces — path-independent work, potential energy defined
  7. 1.3.7Non-conservative forces — friction, air drag
  8. 1.3.8Conservation of mechanical energy — derivation
  9. 1.3.9Power — average and instantaneous, units
  10. 1.3.10Efficiency
  11. 1.3.11Hooke's law — spring force F = −kx
  12. 1.3.12Spring potential energy — derivation
  13. 1.3.13Spring-mass systems — collision problems
1.4

Momentum & Collisions

12 topics
  1. 1.4.1Linear momentum p = mv
  2. 1.4.2Impulse-momentum theorem — derivation
  3. 1.4.3Conservation of linear momentum — derivation from Newton's third law
  4. 1.4.4System with external forces — conditions for conservation
  5. 1.4.5Elastic collisions — 1D - solve for final velocities
  6. 1.4.6Elastic collisions — 2D - angle relationship
  7. 1.4.7Perfectly inelastic collisions — maximum KE loss
  8. 1.4.8Coefficient of restitution e = (v₂ − v₁) - (u₁ − u₂)
  9. 1.4.9Centre of mass — definition for system of particles
  10. 1.4.10Centre of mass — derivation for common shapes (rod, triangle, semicircle, hemisphere)
  11. 1.4.11Motion of centre of mass — external force determines a_CM
  12. 1.4.12Systems with variable mass — rocket equation derivation preview
1.5

Rotational Mechanics

18 topics
  1. 1.5.1Rigid body — definition, degrees of freedom
  2. 1.5.2Angular displacement θ, angular velocity ω, angular acceleration α
  3. 1.5.3Relation to linear quantities - v = rω, a_t = rα, a_c = rω²
  4. 1.5.4Torque τ = r × F — definition, physical meaning
  5. 1.5.5Moment of inertia I = Σmᵢrᵢ² — concept
  6. 1.5.6Parallel axis theorem — I = I_CM + Md² — proof
  7. 1.5.7Perpendicular axis theorem — I_z = I_x + I_y — proof, restrictions
  8. 1.5.8Moment of inertia of - rod (about end, centre), disk, ring, sphere (solid, hollow), cylinder
  9. 1.5.9Rotational kinetic energy = ½Iω²
  10. 1.5.10Angular momentum L = Iω (fixed axis), L = r × p (general)
  11. 1.5.11Torque = dL - dt
  12. 1.5.12Conservation of angular momentum — conditions
  13. 1.5.13Rolling without slipping — v = Rω condition
  14. 1.5.14Rolling KE = ½mv² + ½Iω²
  15. 1.5.15Acceleration of rolling objects on inclines — comparison
  16. 1.5.16Gyroscopic effect — precession of spinning top
  17. 1.5.17Gyroscope in spacecraft attitude control — preview
  18. 1.5.18Equilibrium of rigid bodies — translational + rotational
1.6

Oscillations & Waves

23 topics
  1. 1.6.1Simple harmonic motion — definition, restoring force F = −kx
  2. 1.6.2SHM differential equation — solution - x = A cos(ωt + φ)
  3. 1.6.3ω, T, f relationships
  4. 1.6.4Velocity and acceleration in SHM — v = ω√(A² − x²)
  5. 1.6.5Energy in SHM — KE + PE = ½kA² (constant)
  6. 1.6.6Simple pendulum — small angle approximation, T = 2π√(L - g) derivation
  7. 1.6.7Physical pendulum — compound pendulum
  8. 1.6.8Spring-mass system — horizontal, vertical
  9. 1.6.9Damped oscillations — underdamped, critically damped, overdamped
  10. 1.6.10Q factor — quality of oscillator
  11. 1.6.11Forced oscillations — driving frequency
  12. 1.6.12Resonance — physical consequences, design implications
  13. 1.6.13Mechanical waves — transverse and longitudinal
  14. 1.6.14Wave parameters — amplitude, wavelength, frequency, period, wave speed
  15. 1.6.15Wave equation — derivation for string
  16. 1.6.16Superposition principle
  17. 1.6.17Interference — constructive, destructive conditions
  18. 1.6.18Standing waves — formation, nodes, antinodes
  19. 1.6.19Harmonics and overtones — on strings and in pipes
  20. 1.6.20Beats — derivation, applications
  21. 1.6.21Doppler effect — all cases - source moving, observer moving, both
  22. 1.6.22Shock waves — Mach number, Mach cone — - CRITICAL for rockets -
  23. 1.6.23Sound intensity — decibels (logarithmic scale)
1.7

Thermodynamics

26 topics
  1. 1.7.1Temperature — thermal equilibrium, thermometers, scales
  2. 1.7.2Zeroth law — transitivity of thermal equilibrium
  3. 1.7.3Heat and internal energy — microscopic vs macroscopic
  4. 1.7.4Specific heat capacity — calorimetry
  5. 1.7.5Latent heat — phase transitions
  6. 1.7.6Heat transfer — conduction (Fourier's law k), convection, radiation (Stefan-Boltzmann σT⁴)
  7. 1.7.7Thermal expansion — linear, area, volumetric
  8. 1.7.8Ideal gas law PV = nRT — derivation from kinetic theory
  9. 1.7.9Kinetic theory — pressure derivation, temperature as mean KE
  10. 1.7.10Internal energy of ideal gas U = (f - 2)nRT
  11. 1.7.11Mean free path, mean speed, RMS speed — derivations
  12. 1.7.12Maxwell-Boltzmann speed distribution — derivation (key for propulsion)
  13. 1.7.13First law of thermodynamics — dU = dQ − dW, sign conventions
  14. 1.7.14Thermodynamic processes — isothermal (T const), isochoric (V const), isobaric (P const), adiabatic (Q = 0)
  15. 1.7.15Work done in each process — derivation
  16. 1.7.16Adiabatic relations — PV^γ = const, TV^(γ−1) = const (derivation)
  17. 1.7.17γ = Cp - Cv — for monatomic, diatomic, polyatomic
  18. 1.7.18Second law — Kelvin-Planck statement, Clausius statement
  19. 1.7.19Heat engines — efficiency η = 1 − Q_C - Q_H
  20. 1.7.20Refrigerators and heat pumps — COP
  21. 1.7.21Carnot cycle — full derivation, efficiency = 1 − T_C - T_H
  22. 1.7.22Entropy — Clausius definition dS = dQ_rev - T
  23. 1.7.23Entropy change in irreversible processes — always - 0
  24. 1.7.24Entropy and disorder — Boltzmann S = k·ln(W)
  25. 1.7.25Third law of thermodynamics — S → 0 as T → 0
  26. 1.7.26Thermodynamic potentials — U, H, F, G (preview)
1.8

Electromagnetism

36 topics
  1. 1.8.1Electric charge — properties, quantization, conservation
  2. 1.8.2Coulomb's law — force, comparison with gravity
  3. 1.8.3Superposition principle for forces
  4. 1.8.4Electric field — definition, field lines, superposition
  5. 1.8.5Electric field of point charge, dipole, ring, disk, line charge (Gauss's law)
  6. 1.8.6Gauss's law — integral form, choosing Gaussian surfaces
  7. 1.8.7Applications — sphere, cylinder, infinite plane
  8. 1.8.8Electric potential — definition V = −∫E·dl
  9. 1.8.9Potential of point charge, potential from field and vice versa
  10. 1.8.10Equipotential surfaces — perpendicular to field
  11. 1.8.11Capacitance — parallel plate derivation, cylindrical, spherical
  12. 1.8.12Series and parallel capacitors — derivations
  13. 1.8.13Energy stored in capacitor U = ½CV²
  14. 1.8.14Dielectrics — polarization, dielectric constant, effect on capacitance
  15. 1.8.15Drift velocity, mobility, conductivity
  16. 1.8.16Ohm's law — microscopic origin, resistivity
  17. 1.8.17Series and parallel resistance
  18. 1.8.18Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL)
  19. 1.8.19RC circuits — charging, discharging, time constant τ = RC
  20. 1.8.20Magnetic force on charge — F = qv × B
  21. 1.8.21Magnetic force on current-carrying conductor
  22. 1.8.22Biot-Savart law — magnetic field from current element
  23. 1.8.23Ampere's circuital law — magnetostatic form
  24. 1.8.24Magnetic field of straight wire, circular loop, solenoid, toroid
  25. 1.8.25Magnetic flux Φ = ∫B·dA
  26. 1.8.26Faraday's law — EMF = −dΦ - dt
  27. 1.8.27Lenz's law — opposing induced current
  28. 1.8.28Self-inductance L, mutual inductance M
  29. 1.8.29RL circuit — growth and decay of current
  30. 1.8.30LC circuit — oscillations (electrical analog of SHM)
  31. 1.8.31Maxwell's equations — integral form, all four
  32. 1.8.32Displacement current — Maxwell's addition to Ampere's law
  33. 1.8.33Electromagnetic waves — derivation from Maxwell's equations
  34. 1.8.34Speed of light c = 1 - √(ε₀ μ₀)
  35. 1.8.35EM spectrum — all bands and applications
  36. 1.8.36Poynting vector — energy flux in EM waves

Phase 2 — Advanced Physics

6–8 months @ 2 hrs/day · Begin after Math Phase 3–4.25 chapters
2.1

Analytical Mechanics

25 topics
  1. 2.1.1Constraints — holonomic vs non-holonomic, rheonomic vs scleronomic
  2. 2.1.2Generalized coordinates — choosing them, degrees of freedom
  3. 2.1.3Kinetic energy in generalized coordinates
  4. 2.1.4Lagrangian L = T − V
  5. 2.1.5Derivation of Euler-Lagrange equations from D'Alembert's principle
  6. 2.1.6Applying E-L equations to various systems
  7. 2.1.7Generalized momenta and generalized forces
  8. 2.1.8Cyclic coordinates — corresponding conservation law
  9. 2.1.9Noether's theorem — symmetry ↔ conservation law
  10. 2.1.10Constraints using Lagrange multipliers
  11. 2.1.11Hamiltonian — definition H = Σpᵢq̇ᵢ − L
  12. 2.1.12Hamilton's equations of motion
  13. 2.1.13Phase space — trajectories, phase portraits
  14. 2.1.14Liouville's theorem — phase space volume conservation
  15. 2.1.15Poisson brackets — definition, properties, connection to commutators
  16. 2.1.16Canonical transformations — generating functions
  17. 2.1.17Hamilton-Jacobi equation
  18. 2.1.18Action-angle variables — integrable systems
  19. 2.1.19Principle of least action — Hamilton's principle derivation
  20. 2.1.20Normal modes — coupled oscillators, normal coordinates
  21. 2.1.21Rigid body dynamics — Euler angles, Euler's equations of motion
  22. 2.1.22Inertia tensor — principal axes, principal moments
  23. 2.1.23Torque-free rotation — Euler's equations, asymmetric top
  24. 2.1.24Gyroscope — steady precession derivation
  25. 2.1.25Chaotic systems — sensitivity to initial conditions, Lyapunov exponents
2.2

Fluid Mechanics

30 topics
  1. 2.2.1Fluid definition — shear stress, no fixed shape
  2. 2.2.2Density, specific gravity
  3. 2.2.3Viscosity — dynamic μ, kinematic ν = μ - ρ; Newtonian vs non-Newtonian
  4. 2.2.4Surface tension — origin, Young-Laplace equation
  5. 2.2.5Hydrostatics — pressure = ρgh, derivation
  6. 2.2.6Pascal's law — pressure transmits equally
  7. 2.2.7Buoyancy — Archimedes' principle, derivation from pressure difference
  8. 2.2.8Manometers, barometers
  9. 2.2.9Fluid kinematics — Eulerian vs Lagrangian description
  10. 2.2.10Streamlines, pathlines, streaklines
  11. 2.2.11Stream function, velocity potential
  12. 2.2.12Continuity equation — derivation (conservation of mass), ρAv = const
  13. 2.2.13Reynolds transport theorem
  14. 2.2.14Bernoulli's equation — derivation from F = ma along streamline
  15. 2.2.15Assumptions in Bernoulli — steady, inviscid, incompressible, along streamline
  16. 2.2.16Applications — Pitot tube, Venturi meter, orifice flow
  17. 2.2.17Viscous flow — Poiseuille flow, velocity profile in pipe
  18. 2.2.18Navier-Stokes equations — derivation from Newton's second law for fluid
  19. 2.2.19Reynolds number Re = ρvL - μ — laminar vs turbulent criterion
  20. 2.2.20Boundary layer — Prandtl's concept, growth along flat plate
  21. 2.2.21Boundary layer thickness, displacement thickness, momentum thickness
  22. 2.2.22Blasius solution — exact laminar boundary layer solution
  23. 2.2.23Boundary layer separation — adverse pressure gradient
  24. 2.2.24Drag — pressure (form) drag, skin friction drag
  25. 2.2.25Lift — Kutta-Joukowski theorem L = ρV∞Γ
  26. 2.2.26Dimensional analysis — Buckingham π theorem
  27. 2.2.27Similarity — geometric, kinematic, dynamic; Reynolds similarity
  28. 2.2.28Potential flow — irrotational, inviscid; superposition of basic flows
  29. 2.2.29Vorticity — ω = ∇ × v, circulation Γ
  30. 2.2.30Kelvin's circulation theorem
2.3

Modern Physics

33 topics
  1. 2.3.1Blackbody radiation — Planck's quantum hypothesis
  2. 2.3.2Photoelectric effect — Einstein's explanation, work function
  3. 2.3.3Photon properties — E = hf, p = h - λ
  4. 2.3.4Compton scattering — wavelength shift derivation
  5. 2.3.5De Broglie hypothesis — matter waves λ = h - p
  6. 2.3.6Davisson-Germer experiment — electron diffraction
  7. 2.3.7Heisenberg uncertainty principle — Δx Δp ≥ ℏ - 2, ΔE Δt ≥ ℏ - 2
  8. 2.3.8Wave function ψ — probability density - ψ - ²
  9. 2.3.9Schrödinger equation — time-dependent, time-independent
  10. 2.3.10Particle in a box — solving TISE, energy levels, wavefunctions
  11. 2.3.11Quantum tunneling — concept, transmission coefficient
  12. 2.3.12Hydrogen atom — solving in spherical coordinates
  13. 2.3.13Quantum numbers n, l, mₗ, mₛ
  14. 2.3.14Hydrogen energy levels Eₙ = −13.6 - n² eV
  15. 2.3.15Spectral series — Lyman, Balmer, Paschen
  16. 2.3.16Pauli exclusion principle
  17. 2.3.17Spin — intrinsic angular momentum
  18. 2.3.18Nuclear structure — protons, neutrons, nuclear forces
  19. 2.3.19Binding energy — mass defect, BE per nucleon curve
  20. 2.3.20Nuclear reactions — Q-value calculation
  21. 2.3.21Radioactive decay — alpha, beta, gamma — mechanisms
  22. 2.3.22Decay law — N = N₀ e^(−λt), half-life, activity
  23. 2.3.23Fission — chain reaction, critical mass
  24. 2.3.24Fusion — solar fusion, tokamak (concept)
  25. 2.3.25Special relativity — Michelson-Morley experiment
  26. 2.3.26Postulates of SR
  27. 2.3.27Simultaneity — relativity of simultaneity
  28. 2.3.28Lorentz transformation — derivation
  29. 2.3.29Time dilation — derivation, twin paradox
  30. 2.3.30Length contraction — derivation
  31. 2.3.31Relativistic momentum p = γmv
  32. 2.3.32Mass-energy equivalence E² = (pc)² + (mc²)²
  33. 2.3.33General relativity — equivalence principle, curved spacetime (overview)
2.4

Thermodynamics & Statistical Mechanics (Advanced)

19 topics
  1. 2.4.1Thermodynamic potentials — U (internal), H (enthalpy), F (Helmholtz), G (Gibbs)
  2. 2.4.2Legendre transforms connecting them
  3. 2.4.3Maxwell relations — derivation from each potential
  4. 2.4.4Gibbs-Helmholtz equation
  5. 2.4.5Chemical potential μ = (∂G - ∂N)_{T,P}
  6. 2.4.6Phase equilibrium — Clausius-Clapeyron equation
  7. 2.4.7Phase rule — Gibbs phase rule
  8. 2.4.8Statistical mechanics — microstate, macrostate
  9. 2.4.9Boltzmann's entropy S = k_B ln(Ω)
  10. 2.4.10Canonical ensemble — partition function Z
  11. 2.4.11Average energy from partition function
  12. 2.4.12Free energy from partition function
  13. 2.4.13Maxwell-Boltzmann distribution — full derivation
  14. 2.4.14Equipartition theorem — ½k_BT per quadratic degree of freedom
  15. 2.4.15Quantum statistics — distinguishable vs indistinguishable particles
  16. 2.4.16Bose-Einstein statistics — bosons
  17. 2.4.17Fermi-Dirac statistics — fermions, Fermi energy
  18. 2.4.18Bose-Einstein condensation — concept
  19. 2.4.19Blackbody radiation from statistical mechanics — Planck distribution
2.5

Optics

18 topics
  1. 2.5.1Geometric optics — rectilinear propagation, reflection, refraction
  2. 2.5.2Mirrors — plane, concave, convex; mirror equation 1 - v + 1 - u = 1 - f
  3. 2.5.3Sign convention for mirrors and lenses
  4. 2.5.4Snell's law — derivation from Fermat's principle
  5. 2.5.5Total internal reflection — critical angle derivation
  6. 2.5.6Thin lenses — lens equation, lens maker's equation
  7. 2.5.7Power of a lens, combination of lenses
  8. 2.5.8Optical instruments — human eye, simple microscope, compound microscope, telescope
  9. 2.5.9Aberrations — chromatic, spherical (concepts)
  10. 2.5.10Huygens' principle — wavefront propagation
  11. 2.5.11Young's double slit — fringe width derivation
  12. 2.5.12Thin film interference — reflected and transmitted
  13. 2.5.13Newton's rings — derivation
  14. 2.5.14Diffraction — single slit intensity pattern derivation
  15. 2.5.15Diffraction grating — condition for maxima
  16. 2.5.16Resolving power — Rayleigh criterion
  17. 2.5.17Polarization — Malus's law, Brewster's angle derivation
  18. 2.5.18Birefringence — ordinary and extraordinary rays

Phase 3 — Aerospace Engineering Physics

8–12 months @ 2+ hrs/day · Begin after Math Phase 4 and Physics Phase 26 chapters
3.1

Compressible Flow & Aerodynamics

30 topics
  1. 3.1.1Review of thermodynamics applied to flow — first law for open systems
  2. 3.1.2Stagnation (total) quantities — T₀, P₀, ρ₀ — derivations
  3. 3.1.3Speed of sound — a = √(γRT) — derivation
  4. 3.1.4Mach number M = V - a — subsonic ( - 1), transonic (~1), supersonic ( - 1), hypersonic ( - 5)
  5. 3.1.5Area-velocity relation — dA - A = (M² − 1)(dV - V) — derivation (explains de Laval nozzle)
  6. 3.1.6Area-Mach number relation A - A - = f(M) — isentropic flow
  7. 3.1.7Isentropic flow tables — P - P₀, T - T₀, ρ - ρ₀ as functions of M
  8. 3.1.8Choked flow — condition M = 1 at throat, maximum mass flow
  9. 3.1.9Converging nozzle — subsonic flow, Mach 1 at exit
  10. 3.1.10Converging-diverging (de Laval) nozzle — subsonic, supersonic flow
  11. 3.1.11Normal shock waves — Rankine-Hugoniot relations (all 5) — derivations
  12. 3.1.12Normal shock properties — M₂, P₂ - P₁, T₂ - T₁, ρ₂ - ρ₁, P₀₂ - P₀₁
  13. 3.1.13Oblique shock waves — θ-β-M relation
  14. 3.1.14Shock wave angle, deflection angle
  15. 3.1.15Detached bow shock
  16. 3.1.16Prandtl-Meyer expansion waves — isentropic, supersonic turning
  17. 3.1.17Prandtl-Meyer function ν(M)
  18. 3.1.18Over - under expanded nozzle flows
  19. 3.1.19Airfoil aerodynamics — camber, chord, thickness
  20. 3.1.20Angle of attack, lift coefficient, drag coefficient
  21. 3.1.21Thin airfoil theory — lift per unit span = πρV²(α + 2β - π c)
  22. 3.1.22Finite wing theory — induced drag, Prandtl's lifting line
  23. 3.1.23Aspect ratio — effect on induced drag
  24. 3.1.24Critical Mach number — onset of local supersonic flow
  25. 3.1.25Wave drag — transonic and supersonic
  26. 3.1.26Area rule — Whitcomb's rule for transonic drag reduction
  27. 3.1.27Hypersonic flow — Mach 5+, high temperature effects
  28. 3.1.28Aerodynamic heating — recovery temperature, heat flux
  29. 3.1.29Aerodynamic coefficients — CN, CA, CL, CD, Cm as functions of angle of attack, Mach
  30. 3.1.30Computational aerodynamics — panel method (intro), CFD overview
3.2

Orbital Mechanics & Astrodynamics

40 topics
  1. 3.2.1Two-body problem — equations of motion, reduction to one-body
  2. 3.2.2Conservation of energy and angular momentum in gravitational field
  3. 3.2.3Orbit equation r = p - (1 + e·cos θ) — derivation from equations of motion
  4. 3.2.4Orbit shape from eccentricity — circle (e=0), ellipse (0 - e - 1), parabola (e=1), hyperbola (e - 1)
  5. 3.2.5Kepler's first law — orbits are conic sections
  6. 3.2.6Kepler's second law — equal areas in equal times, from angular momentum conservation
  7. 3.2.7Kepler's third law — T² ∝ a³ — derivation
  8. 3.2.8Orbital elements (Keplerian) — semi-major axis a, eccentricity e, inclination i, RAAN Ω, argument of perigee ω, true ano
  9. 3.2.9Physical meaning of each orbital element
  10. 3.2.10Vis-viva equation v² = GM(2 - r − 1 - a) — derivation
  11. 3.2.11Specific orbital energy ε = −GM - 2a
  12. 3.2.12Specific angular momentum h = √(GMp)
  13. 3.2.13Circular orbit — velocity, period, energy
  14. 3.2.14Kepler's equation M = E − e·sin E — derivation, eccentric anomaly
  15. 3.2.15Solving Kepler's equation — Newton-Raphson iteration
  16. 3.2.16True anomaly from eccentric anomaly
  17. 3.2.17Converting between orbital elements and state vectors (r, v)
  18. 3.2.18Orbit determination — Gauss's method, Gibbs method
  19. 3.2.19Hohmann transfer — derivation, minimum energy transfer
  20. 3.2.20Hohmann Δv calculation — both maneuvers
  21. 3.2.21Bi-elliptic transfer — when it wins over Hohmann
  22. 3.2.22Plane change maneuvers — Δv = 2v·sin(Δi - 2)
  23. 3.2.23Combined maneuvers — optimal split between plane change and velocity change
  24. 3.2.24Gravity assist (slingshot) — patched conic, v-infinity vectors
  25. 3.2.25Sphere of influence — radius derivation
  26. 3.2.26Patched conic method — interplanetary trajectory design
  27. 3.2.27Pork chop plots — Δv vs launch - arrival date
  28. 3.2.28Lambert's problem — connecting two positions in given time
  29. 3.2.29Gauss's method for Lambert's problem
  30. 3.2.30Lagrange points L1–L5 — derivation, stability
  31. 3.2.31Halo orbits — linearized motion near Lagrange points
  32. 3.2.32Three-body problem — restricted (CR3BP), characteristic equation
  33. 3.2.33Orbital perturbations — J2 effect (oblateness), derivation of nodal precession
  34. 3.2.34Atmospheric drag — exponential atmosphere model, orbit decay
  35. 3.2.35Solar radiation pressure
  36. 3.2.36Third-body perturbations
  37. 3.2.37Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya
  38. 3.2.38Groundtrack analysis — swath, revisit
  39. 3.2.39Launch window — phasing with target orbit
  40. 3.2.40Rendezvous and proximity operations — Clohessy-Wiltshire equations
3.3

Rocket Propulsion

50 topics
  1. 3.3.1Tsiolkovsky rocket equation — full first-principles derivation from momentum
  2. 3.3.2Δv = v_e · ln(m₀ - m_f) — understanding each term
  3. 3.3.3Mass ratio m₀ - m_f — why it's so critical
  4. 3.3.4Specific impulse Isp = v_e - g₀ — definition, physical meaning, units
  5. 3.3.5Typical Isp values — solid (~260s), LOX - RP1 (~311s), LOX - LH2 (~450s), ion engines (~3000s)
  6. 3.3.6Thrust equation F = ṁv_e + (P_e − P_a)A_e — derivation
  7. 3.3.7Mass flow rate ṁ and its relation to throat area
  8. 3.3.8Effective exhaust velocity c = v_e + (P_e − P_a)A_e - ṁ
  9. 3.3.9Thrust coefficient C_F = F - (P_c A - ) — derivation
  10. 3.3.10Characteristic velocity c - = P_c A - ṁ — derivation, combustion efficiency measure
  11. 3.3.11Nozzle thermodynamics — isentropic expansion from chamber to exit
  12. 3.3.12Chamber-to-exit relation - all quantities as f(M_e, γ)
  13. 3.3.13Optimum expansion — P_e = P_a for maximum thrust
  14. 3.3.14Over-expanded nozzle — oblique shocks in plume, efficiency loss
  15. 3.3.15Under-expanded nozzle — Prandtl-Meyer expansion, efficiency loss
  16. 3.3.16Altitude compensation methods — nozzle extension, aerospike
  17. 3.3.17De Laval nozzle geometry — conical, bell (Rao contour), 80% bell
  18. 3.3.18Nozzle area ratio ε = A_e - A - — choosing for optimal performance
  19. 3.3.19Combustion thermodynamics — stoichiometry, adiabatic flame temperature
  20. 3.3.20Real gas effects — dissociation, recombination
  21. 3.3.21Characteristic velocity c - and its relation to flame temperature, MW
  22. 3.3.22Staged combustion cycle — full flow, fuel-rich, oxidizer-rich preburners
  23. 3.3.23Gas generator cycle — performance penalty vs simplicity
  24. 3.3.24Expander cycle — hydrogen-cooled nozzle drives turbine
  25. 3.3.25Pressure-fed cycle — simplest, used in upper stages
  26. 3.3.26Electric pump-fed cycle — modern innovation
  27. 3.3.27Turbopump design — centrifugal pump, axial turbine stages, NPSH
  28. 3.3.28Regenerative cooling — heat flux, coolant flow, pressure drop
  29. 3.3.29Film cooling — effectiveness, coverage fraction
  30. 3.3.30Ablative cooling — charring, blowing
  31. 3.3.31Transpiration cooling
  32. 3.3.32Combustion instability — low-frequency (chugging), high-frequency (screaming)
  33. 3.3.33Acoustic modes in combustion chamber — cause of instability
  34. 3.3.34Injector design — impinging, coaxial, swirl injectors
  35. 3.3.35Solid propellants — fuel + oxidizer in polymer matrix
  36. 3.3.36Burn rate r = a·P^n — Vieille's law
  37. 3.3.37Grain geometry — BATES, star, wagon wheel; neutral - progressive - regressive burn
  38. 3.3.38Solid rocket Isp derivation from grain properties
  39. 3.3.39Hybrid engines — advantages, disadvantages
  40. 3.3.40Electric propulsion — thrust, power, Isp trade-off
  41. 3.3.41Ion engine — ionization, acceleration grid, neutralizer
  42. 3.3.42Hall-effect thruster — cross-field discharge, annular channel
  43. 3.3.43FEEP, MEMS thrusters — micro-propulsion
  44. 3.3.44Nuclear thermal propulsion — NTR Isp ~900 s concept
  45. 3.3.45Rocket staging — series staging, parallel staging
  46. 3.3.46Optimal staging — equal mass ratios (for same Isp)
  47. 3.3.47Payload fraction as function of Δv and Isp
  48. 3.3.48Propellant properties — density, freezing point, toxicity, storability
  49. 3.3.49Cryogenic propellants — handling, insulation, boil-off
  50. 3.3.50Hypergolic propellants — N2O4 - UDMH, MMH
3.4

Rocket Flight Mechanics

26 topics
  1. 3.4.1Coordinate systems — Earth-Centered Inertial (ECI), Earth-Centered Earth-Fixed (ECEF), North-East-Down (NED), launch, bo
  2. 3.4.2Transformation between frames — direction cosine matrices
  3. 3.4.3Forces on a rocket in flight — thrust, aerodynamic (normal, axial), gravity
  4. 3.4.4Equations of motion — 3DOF point mass (trajectory analysis)
  5. 3.4.56DOF equations — translational (Newton), rotational (Euler's equations)
  6. 3.4.6Mass properties — CG location, inertia tensor changing with propellant depletion
  7. 3.4.7Aerodynamic coefficients — CA (axial force), CN (normal force), Cm (pitching moment)
  8. 3.4.8Barrowman equations — centre of pressure calculation for finned rockets
  9. 3.4.9Static margin = (XCP − XCG) - d — must be positive (at least 1 caliber)
  10. 3.4.10Static stability — weather-cocking tendency
  11. 3.4.11Dynamic stability — pitch - yaw damping derivatives
  12. 3.4.12Propulsive forces — thrust misalignment, gimbal angle
  13. 3.4.13Gravity turn trajectory — pitch rate from aerodynamic angle of attack = 0
  14. 3.4.14Pitch program — open-loop pitch-over
  15. 3.4.15Trajectory optimization — minimum gravity loss, minimum drag loss
  16. 3.4.16Max-Q — maximum dynamic pressure q = ½ρv²; structural limit
  17. 3.4.17Staging events — separation dynamics, thrust tail-off
  18. 3.4.18Fairing separation — altitude, dynamic pressure requirements
  19. 3.4.19Reentry mechanics — ballistic coefficient β = m - (C_D A)
  20. 3.4.20Reentry corridor — angle of attack constraints
  21. 3.4.21Aerodynamic heating during reentry — stagnation point heat flux Chapman equation
  22. 3.4.22Thermal protection systems — ablators (PICA, SLA), metallic tiles, RCC
  23. 3.4.23Plasma sheath — communications blackout
  24. 3.4.24Aerocapture — using atmosphere to decelerate into orbit
  25. 3.4.25Aerobraking — gradual orbit lowering using atmospheric drag
  26. 3.4.26Terminal landing — propulsive descent, suicide burn
3.5

Guidance, Navigation & Control (GNC)

55 topics
  1. 3.5.1Reference frames — body frame, inertial frame; rotation between them
  2. 3.5.2Euler angles — roll φ, pitch θ, yaw ψ; rotation sequence (3-2-1 convention)
  3. 3.5.3Direction cosine matrix (DCM) — construction from Euler angles
  4. 3.5.4DCM kinematics — Ċ = −[ω×]C
  5. 3.5.5Gimbal lock — problem with Euler angles at θ = ±90°
  6. 3.5.6Quaternions — definition q = (q₀, q₁, q₂, q₃), unit quaternion constraint
  7. 3.5.7Quaternion product — Hamilton product
  8. 3.5.8Quaternion rotation formula — rotating vector v by quaternion q
  9. 3.5.9Quaternion kinematics — q̇ = ½ Ξ(q) ω
  10. 3.5.10Converting between DCM, quaternions, Euler angles
  11. 3.5.11Modified Rodrigues parameters — singularity-free, compact
  12. 3.5.12Attitude estimation — triad method (two vector measurements)
  13. 3.5.13Inertial navigation — accelerometer measures non-gravitational specific force
  14. 3.5.14Gyroscope — angular velocity measurement, bias, noise
  15. 3.5.15IMU — integrated accelerometer + gyroscope
  16. 3.5.16Mechanization equations — integrating IMU to get position, velocity, attitude
  17. 3.5.17INS error propagation — error state equations
  18. 3.5.18GPS — pseudorange, trilateration, dilution of precision
  19. 3.5.19GNSS — GPS, GLONASS, Galileo, BeiDou
  20. 3.5.20Sensor fusion — complementary filter (simple), Kalman filter (optimal)
  21. 3.5.21Kalman filter derivation — predict step, update step
  22. 3.5.22Kalman gain — minimizes trace of covariance
  23. 3.5.23Observability — when KF can estimate state
  24. 3.5.24Extended Kalman Filter (EKF) — linearization, Jacobians
  25. 3.5.25Unscented Kalman Filter (UKF) — sigma points, better for nonlinear
  26. 3.5.26Control system fundamentals — plant, actuator, sensor, controller
  27. 3.5.27Transfer function — Laplace domain, poles and zeros
  28. 3.5.28Block diagram algebra
  29. 3.5.29State-space representation — x' = Ax + Bu, y = Cx + Du
  30. 3.5.30Eigenvalues of A — system modes, stability
  31. 3.5.31Lyapunov stability — Lyapunov function, positive definiteness
  32. 3.5.32Controllability matrix — rank test
  33. 3.5.33Observability matrix — rank test
  34. 3.5.34Pole placement — Ackermann's formula
  35. 3.5.35Linear Quadratic Regulator (LQR) — Riccati equation, optimal gains
  36. 3.5.36LQG — LQR + Kalman filter, separation principle
  37. 3.5.37H∞ control — robust to uncertainty (intro)
  38. 3.5.38PID control — proportional, integral, derivative terms
  39. 3.5.39PID tuning — Ziegler-Nichols, loop shaping
  40. 3.5.40Root locus — Evans' method, rules for sketching
  41. 3.5.41Bode plot — magnitude and phase vs frequency
  42. 3.5.42Gain margin, phase margin — stability margins
  43. 3.5.43Nyquist stability criterion — encirclements of −1
  44. 3.5.44Thrust vector control — single-gimbal, dual-gimbal; TVC angles
  45. 3.5.45TVC dynamics — gimbal servo bandwidth, time delay
  46. 3.5.46Reaction control system — thruster selection, plume impingement limits
  47. 3.5.47Attitude control modes — spin stabilization, 3-axis active
  48. 3.5.48Reaction wheels — momentum management, zero-crossing
  49. 3.5.49Control moment gyroscopes (CMG) — high torque, singularity
  50. 3.5.50Proportional navigation guidance — N·V_c·λ̇, derivation
  51. 3.5.51Augmented proportional navigation — gravity compensation
  52. 3.5.52Optimal guidance — ZEM - ZEV formulation
  53. 3.5.53Powered descent guidance — G-FOLD algorithm (convex optimization)
  54. 3.5.54Terminal descent — velocity vector alignment, touchdown constraints
  55. 3.5.55Autonomous GNC for reusable rockets — SpaceX approach overview
3.6

Spacecraft Structures & Systems Engineering

35 topics
  1. 3.6.1Structural loads — axial (thrust), bending (wind shear), dynamic (vibration, acoustics, shock)
  2. 3.6.2Structural design process — load cases, FOS (factor of safety)
  3. 3.6.3Stress and strain — σ = F - A, ε = ΔL - L, Young's modulus E
  4. 3.6.4Hooke's law in 3D — generalized stress-strain (tensor)
  5. 3.6.5Yield stress, ultimate stress — material behavior
  6. 3.6.6Buckling — Euler column buckling load derivation
  7. 3.6.7Shell buckling — thin-walled cylinder under axial load
  8. 3.6.8Fatigue — S-N curves, Miner's rule
  9. 3.6.9Fracture mechanics — stress intensity factor K, toughness K_IC
  10. 3.6.10Modal analysis — natural frequencies, mode shapes
  11. 3.6.11Random vibration — PSD, RMS acceleration
  12. 3.6.12Acoustic loads — SPL, octave band analysis
  13. 3.6.13Shock response spectrum (SRS)
  14. 3.6.14Thermal analysis — conduction in structures, thermal stress
  15. 3.6.15Composite materials — fiber-matrix, ply properties, laminate theory
  16. 3.6.16Classical laminate theory — ABD matrix
  17. 3.6.17Sandwich structures — face sheets, core
  18. 3.6.18Finite element method — nodes, elements, stiffness matrix
  19. 3.6.19FEM for structures — assembling global stiffness
  20. 3.6.20FEM software — NASTRAN, ABAQUS (concepts and use)
  21. 3.6.21Spacecraft bus — structure, power, thermal, ADCS, C&DH, comms, propulsion
  22. 3.6.22Power systems — solar arrays (I-V curve, power tracking), batteries (DoD, cycles), RTG
  23. 3.6.23Thermal control — multi-layer insulation (MLI), heaters, heat pipes, radiators
  24. 3.6.24Mass budgets — dry mass, wet mass, margin
  25. 3.6.25Link budget — path loss, EIRP, G - T, Eb - N0
  26. 3.6.26Systems engineering — V-model, requirements traceability
  27. 3.6.27Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable)
  28. 3.6.28Verification methods — analysis, test, inspection, demonstration
  29. 3.6.29FMEA — failure mode, effect, severity, detection, RPN
  30. 3.6.30Fault tree analysis (FTA) — top-down, AND - OR gates
  31. 3.6.31Reliability — MTTF, MTBF, exponential failure model
  32. 3.6.32Redundancy — cold standby, hot standby, active redundancy
  33. 3.6.33Environmental testing — thermal vacuum (TVAC), vibration, acoustic, EMC - EMI
  34. 3.6.34Space environment — LEO radiation (SAA, Van Allen), atomic oxygen, MMOD debris
  35. 3.6.35Radiation effects — TID, SEE, displacement damage