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Inverted Pendulum
An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and without additional help will fall over. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balancer With Wine 3
Balancer are a hybrid breed of beef cattle, a combination of Gelbvieh and Angus. These cattle are bred for their hybrid vigour Heterosis, hybrid vigor, or outbreeding enhancement is the improved or increased function of any biological quality in a hybrid offspring. An offspring is heterotic if its traits are enhanced as a result of mixing the genetic contributions of ..., resulting in a higher growth rate and better quality meat. ReferencesBreed Benefits{{cattle-stub Cattle breeds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Networks
A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting from e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-dimensional
In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, often in the plane. Euclidean geometry Euclid set forth the first great landmark of mathematical thought, an axiomati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pendulum (mathematics)
A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations. Simple gravity pendulum A ''simple gravity pendulum'' is an idealized mathematical model of a real pendulum. This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. Since in this model there is no frictional energy loss, when given an initial displacement it wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3 More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.''Analytical Mechanics'', L.N. Hand, J.D. Finch, Cambridge University Press, 2008, The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathieu Equation
In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation : \frac + (a - 2q\cos(2x))y = 0, where a and q are parameters. They were first introduced by Émile Léonard Mathieu, who encountered them while studying vibrating elliptical drumheads.Morse and Feshbach (1953).Brimacombe, Corless and Zamir (2021) They have applications in many fields of the physical sciences, such as optics, quantum mechanics, and general relativity. They tend to occur in problems involving periodic motion, or in the analysis of partial differential equation boundary value problems possessing elliptic symmetry.Gutiérrez-Vega (2015). Definition Mathieu functions In some usages, ''Mathieu function'' refers to solutions of the Mathieu differential equation for arbitrary values of a and q. When no confusion can arise, other authors use the term to refer specifically to \pi- or 2\pi-periodic solutions, which exist only for special valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Harmonic Motion
In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position. It results in an oscillation, described by a sinusoid which continues indefinitely, if uninhibited by friction or any other dissipation of energy. Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillation
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kapitza's Pendulum
Kapitza's pendulum or Kapitza pendulum is a rigid pendulum in which the pivot point vibrates in a vertical direction, up and down. It is named after Russian Nobel prize, Nobel laureate physicist Pyotr Kapitza, who in 1951 developed a theory which successfully explains some of its unusual properties.; The unique feature of the Kapitza pendulum is that the vibrating suspension can cause it to balance stably in an inverted pendulum, inverted position, with the bob above the suspension point. In the usual Pendulum (mathematics), pendulum with a fixed suspension, the only stable equilibrium position is with the bob hanging below the suspension point; the inverted position is a point of Mechanical equilibrium, unstable equilibrium, and the smallest perturbation moves the pendulum out of equilibrium. In nonlinear control theory the Kapitza pendulum is used as an example of a parametric oscillator that demonstrates the concept of "dynamic stabilization". The pendulum was first described b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-balancing Unicycle
An electric unicycle (often initialized as EUC or acronymized yuke or Uni) is a self-balancing personal transporter with a single wheel. The rider controls speed by leaning forwards or backwards, and steers by twisting or tilting the unit side to side. The self-balancing mechanism uses accelerometers, gyroscopes, and a magnetometer. In 2020, suspension models were introduced by three major manufacturers Begode, Kingsong and Inmotion. Operation Commercial units are self-balancing in a forward and backward direction, with side-to-side (lateral) stability being provided by the steering motions of the rider, similar to Bicycle and motorcycle dynamics. As of 2022, no commercial human-rideable unicycle has lateral self-balancing capabilities. However, a non-ridable, dual-axis self-balancing unicycle was demonstrated in 2012, with small, lightweight robots using a large weighted reaction wheel or control moment gyroscope. The control of a unicycle can be considered to be an inverte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-balancing Scooter
A self-balancing scooter (also hoverboard, self-balancing board, segway or electric scooter board) is a self-balancing personal transporter consisting of two motorized wheels connected to a pair of articulated pads on which the rider places their feet. The rider controls the speed by leaning forward or backward, and direction of travel by twisting the pads. Invented in its current form in early 2013, the device is the subject of complex patent disputes. Volume manufacture started in China in 2014 and early units were prone to catching fire due to an overheating battery which resulted in product recalls in 2016, including over 500,000 units sold in the United States by eight manufacturers. History Shane Chen, an American businessman and founder of Inventist filed a patent for a device of this type in February 2013 and launched a Kickstarter fund-raising campaign in May 2013. The devices' increasing popularity in Western countries has been attributed, initially, to endorsement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Segway PT
The Segway is a two-wheeled, self-balancing personal transporter invented by Dean Kamen and brought to market in 2001 as the Segway HT, subsequently as the Segway PT, and manufactured by Segway Inc. ''HT'' is an initialism for "human transporter" and ''PT'' for "personal transporter." Ninebot, a Beijing-based transportation robotics startup rival, acquired Segway Inc. in April 2015, broadened the company to include other transportation devices, and announced in June 2020 it would no longer make a two-wheeled, self-balancing product. History Independent company The Segway PT, referred to during development and initial marketing as the Segway HT, was developed from the self-balancing iBOT wheelchair which was initially developed at University of Plymouth, in conjunction with BAE Systems and Sumitomo Precision Products. Segway's first patent was filed in 1994 and granted in 1997, followed by others, including one submitted in June 1999 and granted in October 2001. Prior to i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
