Ballistic missileA ballistic missile is a type of missile that uses projectile motion to deliver warheads on a target. These weapons are powered only during relatively brief periods—most of the flight is unpowered. Short-range ballistic missiles stay within the Earth's atmosphere, while intercontinental ballistic missiles (ICBMs) are launched on a sub-orbital flight. These weapons are in a distinct category from cruise missiles, which are aerodynamically guided in powered flight.
Anti-ballistic missileAn anti-ballistic missile (ABM) is a surface-to-air missile designed to counter ballistic missiles (missile defense). Ballistic missiles are used to deliver nuclear, chemical, biological, or conventional warheads in a ballistic flight trajectory. The term "anti-ballistic missile" is a generic term conveying a system designed to intercept and destroy any type of ballistic threat; however, it is commonly used for systems specifically designed to counter intercontinental ballistic missiles (ICBMs).
Intercontinental ballistic missileAn intercontinental ballistic missile (ICBM) is a ballistic missile with a range greater than , primarily designed for nuclear weapons delivery (delivering one or more thermonuclear warheads). Conventional, chemical, and biological weapons can also be delivered with varying effectiveness, but have never been deployed on ICBMs. Most modern designs support multiple independently targetable reentry vehicle (MIRVs), allowing a single missile to carry several warheads, each of which can strike a different target.
Submarine-launched ballistic missileA submarine-launched ballistic missile (SLBM) is a ballistic missile capable of being launched from submarines. Modern variants usually deliver multiple independently targetable reentry vehicles (MIRVs), each of which carries a nuclear warhead and allows a single launched missile to strike several targets. Submarine-launched ballistic missiles operate in a different way from submarine-launched cruise missiles.
BallisticsBallistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance. A ballistic body is a free-moving body with momentum which can be subject to forces such as the forces exerted by pressurized gases from a gun barrel or a propelling nozzle, normal force by rifling, and gravity and air drag during flight.
Projectile motionProjectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible. The curved path of objects in projectile motion was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upward or downward.
Sub-orbital spaceflightA sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the surface of the gravitating body from which it was launched. Hence, it will not complete one orbital revolution, will not become an artificial satellite nor will it reach escape velocity. For example, the path of an object launched from Earth that reaches the Kármán line (about – above sea level), and then falls back to Earth, is considered a sub-orbital spaceflight.
Ballistic coefficientIn ballistics, the ballistic coefficient (BC, C_b) of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the negative acceleration: a high number indicates a low negative acceleration—the drag on the body is small in proportion to its mass. BC can be expressed with the units kilograms per square meter (kg/m2) or pounds per square inch (lb/in2) (where 1 lb/in2 corresponds to 703.069581kg/m2).
De Broglie–Bohm theoryThe de Broglie–Bohm theory, also known as the pilot wave theory, Bohmian mechanics, Bohm's interpretation, and the causal interpretation, is an interpretation of quantum mechanics. In addition to the wavefunction, it also postulates an actual configuration of particles exists even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation.
Exponential growthExponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth).
Celestial mechanicsCelestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics.
Exponential functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers.
Hydrodynamic quantum analogsIn physics, the hydrodynamic quantum analogs refer to experimentally-observed phenomena involving bouncing fluid droplets over a vibrating fluid bath that behave analogously to several quantum-mechanical systems. A droplet can be made to bounce indefinitely in a stationary position on a vibrating fluid surface. This is possible due to a pervading air layer that prevents the drop from coalescing into the bath.
Matrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .
Exponential decayA quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: The solution to this equation (see derivation below) is: where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0.
MotionIn physics, motion is the phenomenon by which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.
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.
Wave equationThe (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.
Motion estimationMotion estimation is the process of determining motion vectors that describe the transformation from one 2D image to another; usually from adjacent frames in a video sequence. It is an ill-posed problem as the motion is in three dimensions but the images are a projection of the 3D scene onto a 2D plane. The motion vectors may relate to the whole image (global motion estimation) or specific parts, such as rectangular blocks, arbitrary shaped patches or even per pixel.
Schrödinger equationThe Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics.
