Rotation formalisms in three dimensionsIn geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is described with the same tools, as it is defined as an imaginary rotation from a reference placement in space, rather than an actually observed rotation from a previous placement in space.
Quaternions and spatial rotationUnit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis.
Federal ReserveThe Federal Reserve System (often shortened to the Federal Reserve, or simply the Fed) is the central banking system of the United States. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a series of financial panics (particularly the panic of 1907) led to the desire for central control of the monetary system in order to alleviate financial crises. Over the years, events such as the Great Depression in the 1930s and the Great Recession during the 2000s have led to the expansion of the roles and responsibilities of the Federal Reserve System.
Federal republicA federal republic is a federation of states with a republican form of government. At its core, the literal meaning of the word republic when used to reference a form of government means: "a country that is governed by elected representatives and by an elected leader (such as a president) rather than by a monarch". In a federal republic, a division of powers exists between the federal government and the government of the individual subdivisions.
Federal government of the United StatesThe federal government of the United States (U.S. federal government or U.S. government) is the national government of the United States, a federal republic located primarily in North America, composed of 50 states, five major self-governing territories, several island possessions, and the federal district and national capital of Washington, D.C., where most of the federal government is based. The U.S. federal government, sometimes simply referred to as "Washington", is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.
