Moment of inertiaThe moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.
Kinetic energyIn physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
Equations of motionIn physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.
InertiaInertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law of motion. After some other definitions, Newton states in his first law of motion: LAW I. Every object perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Rotational energyRotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed: where The mechanical work required for or applied during rotation is the torque times the rotation angle. The instantaneous power of an angularly accelerating body is the torque times the angular velocity.
Moment (physics)In physics, a moment is a mathematical expression involving the product of a distance and physical quantity. Moments are usually defined with respect to a fixed reference point and refer to physical quantities located some distance from the reference point. In this way, the moment accounts for the quantity's location or arrangement. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object.
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.
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.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Rigid bodyIn physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light.
Euler equations (fluid dynamics)In fluid dynamics, the Euler equations are a set of quasilinear partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity. The Euler equations can be applied to incompressible or compressible flow. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together with the incompressibility condition that the flow velocity is a solenoidal field.
Archimedean solidIn geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are composed of only one type of polygon), excluding the prisms and antiprisms, and excluding the pseudorhombicuboctahedron. They are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices.
Platonic solidIn geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra: Geometers have studied the Platonic solids for thousands of years. They are named for the ancient Greek philosopher Plato who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids.
Allgemeine SSThe Allgemeine SS (ˌalɡəˈmaɪ̯nə ˈɛs ˈɛs; "General SS") was a major branch of the Schutzstaffel (SS) paramilitary forces of Nazi Germany; it was managed by the SS Main Office (SS-Hauptamt). The Allgemeine SS was officially established in the autumn of 1934 to distinguish its members from the SS-Verfügungstruppe (SS Dispositional Troops or SS-VT), which later became the Waffen-SS, and the SS-Totenkopfverbände (SS Death's Head Units or SS-TV), which were in charge of the Nazi concentration camps and extermination camps.
Waffen-SSThe Waffen-SS (ˈvafn̩ʔɛsˌʔɛs) (Armed SS) was the combat branch of the Nazi Party's paramilitary Schutzstaffel (SS) organisation. Its formations included men from Nazi Germany, along with volunteers and conscripts from both occupied and unoccupied lands. The Waffen-SS grew from three regiments to over 38 divisions during World War II, and served alongside the German Army (Heer), Ordnungspolizei (Order Police), and other security units.
Battle axeA battle axe (also battle-axe, battle ax, or battle-ax) is an axe specifically designed for combat. Battle axes were specialized versions of utility axes. Many were suitable for use in one hand, while others were larger and were deployed two-handed. Axes designed for warfare ranged in weight from just over , and in length from just over to upwards of , as in the case of the Danish axe or the sparth axe. Cleaving weapons longer than 150 cm would arguably fall into the category of polearms.
PARI/GPPARI/GP is a computer algebra system with the main aim of facilitating number theory computations. Versions 2.1.0 and higher are distributed under the GNU General Public License. It runs on most common operating systems. The PARI/GP system is a package that is capable of doing formal computations on recursive types at high speed; it is primarily aimed at number theorists. Its three main strengths are its speed, the possibility of directly using data types that are familiar to mathematicians, and its extensive algebraic number theory module.
GP-5 gas maskThe GP-5 gas mask kit (Гражда́нский Противога́з-5) is a Soviet-made gas mask kit, which contains a single-filter ShM-62 or Shm-62U gas mask. It was issued to the Soviet population starting in 1962; production ended in 1990. It is a lightweight mask, weighing 1.09 kg (2.42 lbs). It can operate in all weather and withstand temperatures from to . The ShM-62 or comes with sealed glass eye pieces. The GP-5 kit was originally made to protect the wearer from radioactive fallout during the Cold War and were distributed to most fallout shelters.
LabrysLabrys (lábrys) is, according to Plutarch (Quaestiones Graecae 2.302a), the Lydian word for the double-bitted axe. In Greek it was called πέλεκυς (pélekys). The plural of labrys is labryes (λάβρυες). Plutarch relates that the word labrys was a Lydian word for 'axe': Λυδοὶ γὰρ ‘λάβρυν’ τὸν πέλεκυν ὀνομάζουσι . ("For Lydians name the double-edged axe 'Labyrs'"). Many scholars including Arthur Evans assert that the word labyrinth is derived from labrys and thus implies 'house of the double axe'.
SchutzstaffelThe Schutzstaffel (SS; also stylized as ᛋᛋ with Armanen runes; ˈʃʊtsˌʃtafl̩; Protection Squadron) was a major paramilitary organization under Adolf Hitler and the Nazi Party in Nazi Germany, and later throughout German-occupied Europe during World War II. It began with a small guard unit known as the Saal-Schutz ("Hall Security") made up of party volunteers to provide security for party meetings in Munich. In 1925, Heinrich Himmler joined the unit, which had by then been reformed and given its final name.
