Euler's equations (rigid body dynamics)In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. Their general vector form is where M is the applied torques and I is the inertia matrix. The vector is the angular acceleration. Again, note that all quantities are defined in the rotating reference frame.
Fick's laws of diffusionFick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.
Poinsot's ellipsoidIn classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of the angular momentum, expressed with respect to an inertial laboratory frame. The angular velocity vector of the rigid rotor is not constant, but satisfies Euler's equations.
Set-theoretic definition of natural numbersIn set theory, several ways have been proposed to construct the natural numbers. These include the representation via von Neumann ordinals, commonly employed in axiomatic set theory, and a system based on equinumerosity that was proposed by Gottlob Frege and by Bertrand Russell. Zermelo ordinals In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and n + 1 = n ∪ {n} for each n. In this way n = {0, 1, ..., n − 1} for each natural number n.
IceboatAn iceboat (occasionally spelled ice boat or traditionally called an ice yacht) is a recreational or competition sailing craft supported on metal runners for traveling over ice. One of the runners is steerable. Originally, such craft were boats with a support structure, riding on the runners and steered with a rear blade, as with a conventional rudder. As iceboats evolved, the structure became a frame with a seat or cockpit for the iceboat sailor, resting on runners. Steering was shifted to the front.
Inverse distance weightingInverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I). The name given to this type of method was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights.
Non-well-founded set theoryNon-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as an axiom.
TrimaranA trimaran (or double-outrigger) is a multihull boat that comprises a main hull and two smaller outrigger hulls (or "floats") which are attached to the main hull with lateral beams. Most modern trimarans are sailing yachts designed for recreation or racing; others are ferries or warships. They originated from the traditional double-outrigger hulls of the Austronesian cultures of Maritime Southeast Asia; particularly in the Philippines and Eastern Indonesia, where it remains the dominant hull design of traditional fishing boats.
Solar sailSolar sails (also known as lightsails, light sails, and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight on large surfaces. A number of spaceflight missions to test solar propulsion and navigation have been proposed since the 1980s. The first spacecraft to make use of the technology was IKAROS, launched in 2010. A useful analogy to solar sailing may be a sailing boat; the light exerting a force on the large surface is akin to a sail being blown by the wind.
Bermuda rigA Bermuda rig, Bermudian rig, or Marconi rig is a configuration of mast and rigging for a type of sailboat and is the typical configuration for most modern sailboats. This configuration was developed in Bermuda in the 1600s; the term Marconi, a reference to the inventor of the radio, Guglielmo Marconi, became associated with this configuration in the early 1900s because the wires that stabilize the mast of a Bermuda rig reminded observers of the wires on early radio masts.
