Generalizations of the derivativeIn mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, geometry, etc. The Fréchet derivative defines the derivative for general normed vector spaces . Briefly, a function , an open subset of , is called Fréchet differentiable at if there exists a bounded linear operator such that Functions are defined as being differentiable in some open neighbourhood of , rather than at individual points, as not doing so tends to lead to many pathological counterexamples.
Battle of the BeamsThe Battle of the Beams was a period early in the Second World War when bombers of the German Air Force (Luftwaffe) used a number of increasingly accurate systems of radio navigation for night bombing in the United Kingdom. British scientific intelligence at the Air Ministry fought back with a variety of their own increasingly effective means, involving jamming and deception signals. The period ended when the Wehrmacht moved their forces to the East in May 1941, in preparation for the attack on the Soviet Union.
Lie derivativeIn differential geometry, the Lie derivative (liː ), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate invariant and therefore the Lie derivative is defined on any differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field, then the Lie derivative of T with respect to X is denoted .
Spin–orbit interactionIn quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus.
Phase detectorA phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a signal which represents the difference in phase between two signal inputs. The phase detector is an essential element of the phase-locked loop (PLL). Detecting phase difference is important in other applications, such as motor control, radar and telecommunication systems, servo mechanisms, and demodulators. Phase detectors for phase-locked loop circuits may be classified in two types.
Spacecraft attitude controlSpacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, etc. Controlling vehicle attitude requires sensors to measure vehicle orientation, actuators to apply the torques needed to orient the vehicle to a desired attitude, and algorithms to command the actuators based on (1) sensor measurements of the current attitude and (2) specification of a desired attitude.
Direction findingDirection finding (DF), or radio direction finding (RDF), is - in accordance with International Telecommunication Union (ITU) - defined as radio location that uses the reception of radio waves to determine the direction in which a radio station or an object is located. This can refer to radio or other forms of wireless communication, including radar signals detection and monitoring (ELINT/ESM). By combining the direction information from two or more suitably spaced receivers (or a single mobile receiver), the source of a transmission may be located via triangulation.
Covariant derivativeIn mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent space.
Phase-locked loopA phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator's frequency and phase are controlled proportionally by an applied voltage, hence the term voltage-controlled oscillator (VCO).
Gimbal lockGimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space. The term gimbal-lock can be misleading in the sense that none of the individual gimbals are actually restrained. All three gimbals can still rotate freely about their respective axes of suspension.
