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Inverted Pendulum
An inverted pendulum is a pendulum that has its center of mass above its Lever, pivot point. It is unstable equilibrium, unstable and falls over without additional help. 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 (mechanics), 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 Degrees of freedom (mechanics), degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downward, an inverted pendulum is inherently unstab ... [...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 Aberdeen Angus, Angus. These cattle are bred for their hybrid vigour, resulting in a higher growth rate and better quality meat. ReferencesBreed Benefits {{cattle-stub Cattle breeds ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected units or nodes called '' artificial neurons'', which loosely model the neurons in the brain. Artificial neuron models that mimic biological neurons more closely have also been recently investigated and shown to significantly improve performance. These are connected by ''edges'', which model the synapses in the brain. Each artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons. The "signal" is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the '' activation function''. The strength of the signal at each connection is determined by a ''weight'', which adjusts during the learning process. Typically, ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-dimensional
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called '' planes'', or, more generally, ''surfaces''. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical positions, like an affine plane or complex plane. Flat The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured. The space is flat because any two lines transversed by a third line perpendicular to both of them are parallel, meaning they nev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pendulum (mathematics)
A pendulum is a body suspended from a fixed support such that it freely swings 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 towards 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 gravity pendulum, 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. It is a weight (or Bob (physics), bob) on the end of a massless cord suspended from a wikt:pivot, pivot, without friction. Since in the model there is no frictional en ... [...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. 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. 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 describing the motion of the dynamics. Types There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term ... [...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 are real-valued parameters. Since we may add to to change the sign of , it is a usual convention to set . 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 (PDE) 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Harmonic Motion
In mechanics and physics, simple harmonic motion (sometimes abbreviated as ) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is 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, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the dis ... [...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 ... [...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 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 position, with the bob above the suspension point. In the usual 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 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 by Andrew Stephenson in 1908, who found that the upper vertical posit ... [...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 unicycle, 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 and gyroscopes. Most manufacturers of EUCs are based out of China, including Segway, Inmotion, Kingsong, Begode, and Leaperkim. Operation Similar to Self-balancing scooter, hoverboards, Onewheels, and Segways, electric unicycles are self-balancing in a forward and backward direction, with side-to-side (lateral) stability being provided by human steering motions that tilt or twist the unit, similar to Bicycle and motorcycle dynamics. The control of a unicycle can be considered to be similar to an inverted pendulum. Many electric unicycles have suspension, either operated by air or springs. Electric unicycles come in varying speeds, battery capacities, and motor wattages. L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-balancing Scooter
A self-balancing scooter (also hoverboard, self-balancing board, electric scooter board, or swegway) 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 infringement, 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. There have been 23 official recalls since 2016, affecting around 1,115,200 units in total. History Shane Chen, a China, Chinese businessman and founder of Inventist filed a patent for a device of this type in February 2013 and launched a Kickstarter fund-raising campaign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Segway PT
A Segway is a two-wheeled, self-balancing personal transporter device invented by Dean Kamen. The name is a registered trademark of Segway Inc. It was brought to market in 2001 as the Segway HT, and then subsequently as the Segway PT. ''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, broadening the company to include other transportation devices. In June 2020, it was announced that it would no longer make the Segway PT. 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. The first patent of human transporter was filed in 1994 and granted in 1997, followed by others, including one submitted in June 1999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
