Proper velocityIn relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector and proper time τ elapsed on the clocks of the traveling object: It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer. The two types of velocity, ordinary and proper, are very nearly equal at low speeds. However, at high speeds proper velocity retains many of the properties that velocity loses in relativity compared with Newtonian theory.
Fourth, fifth, and sixth derivatives of positionIn physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. Unlike the first three derivatives, the higher-order derivatives are less common, thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics and is implemented in MATLAB. The fourth derivative is often referred to as snap or jounce.
Mobile phone trackingMobile phone tracking is a process for identifying the location of a mobile phone, whether stationary or moving. Localization may be affected by a number of technologies, such as the multilateration of radio signals between (several) cell towers of the network and the phone or by simply using GNSS. To locate a mobile phone using multilateration of mobile radio signals, the phone must emit at least the idle signal to contact nearby antenna towers and does not require an active call.
Error analysis for the Global Positioning SystemThe error analysis for the Global Positioning System is important for understanding how GPS works, and for knowing what magnitude of error should be expected. The GPS makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected. GPS receiver position is computed based on data received from the satellites. Errors depend on geometric dilution of precision and the sources listed in the table below. User equivalent range errors (UERE) are shown in the table.
Exploratory data analysisIn statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling and thereby contrasts traditional hypothesis testing. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments.
KinematicsKinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system.
Complete metric spaceIn mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g. is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below).
Functional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces.
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.
