THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Harmonic series
The ladder of integer-multiple frequencies that a bounded system supports above its fundamental.
Hertzian dipole
The idealised point-dipole antenna — an infinitesimally short conductor of length L ≪ λ carrying a uniform oscillating current I(t) = I₀ cos(ωt). Used as the basic radiating element from which the fields of all more complex antennas are built by superposition.
Hohmann transfer
The most fuel-efficient two-burn manoeuvre for moving between two circular orbits; uses a half-ellipse as the transfer path.
Huygens's principle
Every point on a wavefront acts as a source of secondary spherical wavelets; the envelope of all the wavelets gives the wavefront at the next instant. Christiaan Huygens, 1678; generalised by Fresnel and Kirchhoff.
Hydrostatic
Relating to fluids at rest. In the hydrostatic limit, pressure varies only with depth: dp/dz = −ρg.
Hysteresis loop
The closed curve traced by B (or M) versus H in a ferromagnet under a cycled applied field. Its enclosed area equals the energy dissipated per unit volume per cycle.
Image charge
A fictitious charge placed outside the region of interest whose field, together with the real charge's field, satisfies the conductor's boundary conditions.
Impedance
Z = V/I for a component or network driven at a single frequency, generalising resistance to the complex plane. Z = R + jX, where R is the resistance (dissipative) and X is the reactance (energy-storing).
impulse
The change in momentum delivered by a force acting over a time interval: J = ∫F dt = Δp.
Incompressible flow
Fluid motion in which density is effectively constant. Liquids, and gases at Mach ≪ 1.
Induced charge
The surface charge that appears on a conductor in response to a nearby external charge, redistributed until the conductor's interior field is zero.
inelastic collision
A collision in which kinetic energy is not conserved; the missing energy goes into heat, sound, or deformation.
inertia
The tendency of a body to resist changes in its motion; the first of Newton's three laws.
inertial frame
A reference frame in which Newton's laws hold in their simple form; one that is not itself accelerating.
Inertial navigation
Navigation by integrating a vehicle's own rotations and accelerations — no external reference needed.
invariance
The property of a physical quantity or law of remaining unchanged under a specified transformation.
Invariant interval
The Lorentz-scalar combination s² = c²Δt² − Δx² − Δy² − Δz² between any two events. Invariant under Lorentz boosts and rotations; the special-relativistic analogue of Euclidean distance; its sign distinguishes timelike (s² > 0), spacelike (s² < 0), and null (s² = 0) separations.
inverse-square law
Force or intensity that falls as 1/r² with distance; the form of Newton's gravity and Coulomb's law.
isochronism
Property of oscillating with a constant period regardless of amplitude; Galileo's 1583 discovery.
KAM theorem
Most invariant tori of a near-integrable Hamiltonian system survive small perturbations. Proves the solar system is mostly stable.
kinematic equations
The three algebraic relations that describe motion under constant acceleration: v = v₀ + at, x = x₀ + v₀t + ½at², and v² = v₀² + 2a(x − x₀).
kinetic energy
The energy of a body in motion, ½·m·v², measured in joules.
kinetic friction
The friction force acting on a body that is already sliding; has fixed magnitude μ_k · N, independent of speed.
Kirchhoff's current law (KCL)
The sum of currents flowing into any node in a circuit equals the sum of currents flowing out. Equivalently: charge conservation applied to circuit junctions, ∇·J = 0 in steady state.
Kirchhoff's voltage law (KVL)
The sum of voltage drops around any closed loop in a circuit equals zero. Equivalently: the electrostatic field is conservative, ∮E·dℓ = 0 in the quasi-static limit.
Kramers formula
Hendrik Kramers's 1923 classical thick-target bremsstrahlung spectrum, dN/dE ∝ (E_max − E)/E, giving the continuous-continuum shape of an X-ray tube running at accelerating voltage U with E_max = eU. Full treatment in a later branch.
Lagrange points
Five equilibrium positions in the restricted three-body problem where gravitational and centrifugal forces balance.
Lagrangian
The scalar function L = KE − PE whose time-integral (the action) is minimised along the true path of a physical system.
Laminar flow
Orderly flow in parallel layers, without mixing across them. Characteristic of low Reynolds number.
Larmor formula
The classical expression P = q²a²/(6πε₀c³) for the total electromagnetic power radiated by a non-relativistic point charge of acceleration a. Derived by Joseph Larmor in 1897; the foundational result of classical radiation theory.