MomentumIn Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum p (from Latin pellere "push, drive") is: In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second.
Angular momentumIn physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.
Conservation of massIn physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so the quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form.
Mass in special relativityThe word "mass" has two meanings in special relativity: invariant mass (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to rest energy, while relativistic mass is equivalent to relativistic energy (also called total energy).
Invariant massThe invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame".
Center-of-momentum frameIn physics, the center-of-momentum frame (COM frame), also known as zero-momentum frame, is the inertial frame in which the total momentum of the system vanishes. It is unique up to velocity, but not origin. The center of momentum of a system is not a location, but a collection of relative momenta/velocities: a reference frame. Thus "center of momentum" is a short for "center-of-momentum ". A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a single point) remains at the origin.
Finite-state machineA finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition.
Angular momentum operatorIn quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Such an operator is applied to a mathematical representation of the physical state of a system and yields an angular momentum value if the state has a definite value for it.
Momentum operatorIn quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is: where ħ is Planck's reduced constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by ) is used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator.
Orbital angular momentum of lightThe orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. It can be further split into an internal and an external OAM. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront. The external OAM is the origin-dependent angular momentum that can be obtained as cross product of the light beam position (center of the beam) and its total linear momentum.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Deterministic finite automatonIn the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run.
MassMass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent.
Conservation of energyIn physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.
Mass transferMass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation. Mass transfer is used by different scientific disciplines for different processes and mechanisms. The phrase is commonly used in engineering for physical processes that involve diffusive and convective transport of chemical species within physical systems.
Classical mechanicsClassical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The "classical" in "classical mechanics" does not refer classical antiquity, as it might in, say, classical architecture.
Finite difference methodIn numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
ProvenceProvence (prəˈvɒ̃s, USalsoprəʊˈ-, UKalsoprɒˈ-, pʁɔvɑ̃s) is a geographical region and historical province of southeastern France, which extends from the left bank of the lower Rhône to the west to the Italian border to the east; it is bordered by the Mediterranean Sea to the south. It largely corresponds with the modern administrative region of Provence-Alpes-Côte d'Azur and includes the departments of Var, Bouches-du-Rhône, Alpes-de-Haute-Provence, as well as parts of Alpes-Maritimes and Vaucluse.
Nondeterministic finite automatonIn automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and reading an input symbol is required for each state transition. A nondeterministic finite automaton (NFA), or nondeterministic finite-state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article.
Position and momentum spacesIn physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension. Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.
