Degrees of freedom (mechanics)In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields. The position of a single railcar (engine) moving along a track has one degree of freedom because the position of the car is defined by the distance along the track.
Horseshoe mapIn the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced by Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the square, then stretching the result into a long strip, and finally folding the strip into the shape of a horseshoe. Most points eventually leave the square under the action of the map.
Parabolic trajectoryIn astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return.
Inverse kinematicsIn computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics.
Repetitive strain injuryA repetitive strain injury (RSI) is an injury to part of the musculoskeletal or nervous system caused by repetitive use, vibrations, compression or long periods in a fixed position. Other common names include repetitive stress injury, repetitive stress disorders, cumulative trauma disorders (CTDs), and overuse syndrome. Some examples of symptoms experienced by patients with RSI are aching, pulsing pain, tingling and extremity weakness, initially presenting with intermittent discomfort and then with a higher degree of frequency.
Hyperbolic trajectoryIn astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
Object (grammar)In linguistics, an object is any of several types of arguments. In subject-prominent, nominative-accusative languages such as English, a transitive verb typically distinguishes between its subject and any of its objects, which can include but are not limited to direct objects, indirect objects, and arguments of adpositions (prepositions or postpositions); the latter are more accurately termed oblique arguments, thus including other arguments not covered by core grammatical roles, such as those governed by case morphology (as in languages such as Latin) or relational nouns (as is typical for members of the Mesoamerican Linguistic Area).
Radial trajectoryIn astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards or away from each other in a straight line. There are three types of radial trajectories (orbits). Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. The relative speed of the two objects is less than the escape velocity.
SmartwatchA smartwatch is a wearable computer in the form of a watch; modern smartwatches provide a local touchscreen interface for daily use, while an associated smartphone app provides management and telemetry, such as long-term biomonitoring. While early models could perform basic tasks, such as calculations, digital time telling, translations, and game-playing, smartwatches released since 2015 have more general functionality closer to smartphones, including mobile apps, a mobile operating system and WiFi/Bluetooth connectivity.
