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Bond Graph
A bond graph is a graphical representation of a physical dynamic system. It allows the conversion of the system into a state-space representation. It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Bond graphs are multi-energy domain (e.g. mechanical, electrical, hydraulic, etc.) and domain neutral. This means a bond graph can incorporate multiple domains seamlessly. The bond graph is composed of the "bonds" which link together "single-port", "double-port" and "multi-port" elements (see below for details). Each bond represents the instantaneous flow of energy () or power. The flow in each bond is denoted by a pair of variables called power variables, akin to conjugate variables, whose product is the instantaneous power of the bond. The power variables are broken in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - bi. The complex conjugate of z is often denoted as \overline or z^*. In polar form, if r and \varphi are real numbers then the conjugate of r e^ is r e^. This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a^2 + b^2 (or r^2 in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root. Notation The complex conjugate of a complex number z is written as \overline z or z^*. The first notation, a vinculum, avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum (from Latin '' pellere'' "push, drive") is: \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitude (mathematics), magnitude and Direction (geometry, geography), direction of a force are both important, force is a Euclidean vector, vector quantity. The SI unit of force is the newton (unit), newton (N), and force is often represented by the symbol . Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include Elasticity (physics), elastic, frictional, Normal force, contact or "normal" forces, and gravity, gravitational. The rotational version of force is torque, which produces angular acceleration, changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absement
In kinematics, absement (or absition) is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long. The word ''absement'' is a portmanteau of the words ''absence'' and ''displacement''. Similarly, its synonym ''absition'' is a portmanteau of the words ''absence'' and ''position''. Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement. The dimension of absement is length multiplied by time. Its SI unit is meter second (m·s), which corresponds to an object having been displaced by 1 meter for 1 second. This is not to be confused with a meter per second (m/s), a unit of velocity, the time-derivative of position. For example, opening the gate of a gate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical quantity, quantity, meaning that both magnitude and direction are needed to define it. The Scalar (physics), scalar absolute value (Magnitude (mathematics), magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the International System of Units, SI (metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an ''acceleration''. Definition Average velocity The average velocity of an object over a period of time is its Displacement (geometry), change in position, \Delta s, divided by the duration of the period, \Delt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration
In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector quantities (in that they have Magnitude (mathematics), magnitude and Direction (geometry), direction). The orientation of an object's acceleration is given by the orientation of the ''net'' force acting on that object. The magnitude of an object's acceleration, as described by Newton's second law, is the combined effect of two causes: * the net balance of all external forces acting onto that object — magnitude is Direct proportionality, directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is Inverse proportionality, inversely proportional to the object's mass. The International System of Units, SI unit for acceleration is metre per second squared (, \ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerk (physics)
Jerk (also known as jolt) is the rate of change of an object's acceleration over time. It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol and expressed in m/s3 (SI units) or standard gravities per second(''g''0/s). Expressions As a vector, jerk can be expressed as the first time derivative of acceleration, second time derivative of velocity, and third time derivative of position: \mathbf j(t) = \frac = \frac = \frac Where: * is acceleration * is velocity * is position * is time. Third-order differential equations of the form J\left(\overset, \ddot, \dot, x\right) = 0 are sometimes called ''jerk equations''. When converted to an equivalent system of three ordinary first-order non-linear differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour. This condition generates mathematical interest in ''jerk systems''. Systems involving fourth-order derivatives or higher are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Mechanics
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a Hamilton–Jacobi equation, link between classical and quantum mechanics. Overview Phase space coordinates (''p'', ''q'') and Hamiltonian ''H'' Let (M, \mathcal L) be a Lagrangian mechanics, mechanical system with configuration space (physics), configuration space M and smooth Lagrangian_mechanics#Lagrangian, Lagrangian \mathcal L. Select a standard coordinate system (\boldsymbol,\boldsymbol) on M. The quantities \textstyle p_i(\boldsymbol,\boldsymbol,t) ~\stackrel~ / are called ''m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the d'Alembert principle of virtual work. It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, ''Mécanique analytique''. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space (physics), configuration space ''M'' and a smooth function L within that space called a ''Lagrangian''. For many systems, , where ''T'' and ''V'' are the Kinetic energy, kinetic and Potential energy, potential energy of the system, respectively. The stationary action principle requires that the Action (physics)#Action (functional), action functional of the system derived from ''L'' must remain at a stationary point (specifically, a Maximum and minimum, maximum, Maximum and minimum, minimum, or Saddle point, saddle point) throughout the time evoluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Energy
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Robert and Halliday, David (1960) ''Physics'', Section 7-5, Wiley International Edition The kinetic energy of an object is equal to the work, or force ( F) in the direction of motion times its displacement ( s), needed to accelerate the object from rest to its given speed. The same amount of work is done by the object when decelerating from its current speed to a state of rest. The SI unit of energy is the joule, while the English unit of energy is the foot-pound. In relativistic mechanics, \fracmv^2 is a good approximation of kinetic energy only when ''v'' is much less than the speed of light. History and etymology The adjective ''kinetic'' has its roots in the Greek word κίνησις ''kinesis'', meaning "motion". The dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
