THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Gaussian surface
An imaginary closed surface chosen to exploit symmetry when applying Gauss's law.
Generalised coordinates
Any set of independent variables that fully specifies a system's configuration. Not necessarily Cartesian.
Geodesic equation
d²x^μ/dλ² + Γ^μ_{αβ} (dx^α/dλ)(dx^β/dλ) = 0. The trajectory of a freely-falling particle in curved spacetime; the curve whose tangent is parallel-transported along itself. Generalises the Newtonian straight line. In GR, free-fall = geodesic motion.
GPS clock correction
The combined SR + GR clock-rate correction applied by every GPS satellite firmware: kinematic time dilation slows the orbiting clock by ~7 μs/day, gravitational time dilation speeds it up by ~45 μs/day, net correction ~+38 μs/day. Without the correction, position fixes would drift roughly 11 km per day.
Gradient
A vector that points in the direction of steepest increase of a scalar field, with magnitude equal to the rate of that increase.
gravitational field
The vector field g(r) = −GM/r² r̂ giving the acceleration any test mass would experience at each point in space.
gravity assist
Technique in which a spacecraft gains or loses speed by flying close to a planet, exchanging momentum through the planet's gravitational field.
Group velocity
The speed v_g = dω/dk at which a wave packet's envelope — and therefore its energy and information — propagates.
Group velocity (EM)
v_g = dω/dk. The speed at which a wave packet's envelope — and therefore its energy and information content — propagates. In a dispersive medium v_g differs from the phase velocity v_p = ω/k.
H-field
The auxiliary magnetic field H = B/μ₀ − M, in amperes per metre. Its circulation around a loop is determined by free currents only, ignoring bound currents inside magnetised matter.
Hamilton's equations
The first-order system q̇ = ∂H/∂p, ṗ = −∂H/∂q generating time evolution in phase space.
Hamiltonian
A scalar function H(q, p, t) whose partial derivatives, via Hamilton's equations, generate time evolution. For conservative systems, H = T + V.
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.
Holonomy
The rotation a vector picks up when parallel-transported around a closed loop on a manifold. Vanishes if and only if the curvature is zero. On a 2-sphere of radius R, transporting around a loop enclosing area A rotates the vector by A/R² — the spherical-triangle holonomy reveal that motivates the Riemann tensor.
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.