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History Of Classical Mechanics
This article deals with the history of classical mechanics.Contents1 Antiquity 2 Medieval thought 3 Modern age – formation of classical mechanics 4 Present 5 See also 6 Notes 7 ReferencesAntiquity[edit] Main article: Aristotelian physicsAristotle's laws of motion. In Physics
Physics
he states that objects fall at a speed proportional to their weight and inversely proportional to the density of the fluid they are immersed in. This is a correct approximation for objects in Earth's gravitational field moving in air or water.[1]The ancient Greek philosophers, Aristotle
Aristotle
in particular, were among the first to propose that abstract principles govern nature
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Statistical Mechanics
Statistical mechanics
Statistical mechanics
is a branch of theoretical physics that uses probability theory to study the average behaviour of a mechanical system whose exact state is uncertain.[1][2][3][note 1] Statistical mechanics
Statistical mechanics
is commonly used to explain the thermodynamic behaviour of large systems. This branch of statistical mechanics, which treats and extends classical thermodynamics, is known as statistical thermodynamics or equilibrium statistical mechanics. Microscopic mechanical laws do not contain concepts such as temperature, heat, or entropy; however, statistical mechanics shows how these concepts arise from the natural uncertainty about the state of a system when that system is prepared in practice
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Harmonic Oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: F → = − k x → displaystyle vec F =-k vec x , where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:Oscillate with a frequency lower than in the undamped case, and an amplitude decreasing with time (underdamped oscill
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Routhian Mechanics
In analytical mechanics, a branch of theoretical physics, Routhian mechanics is a hybrid formulation of Lagrangian mechanics
Lagrangian mechanics
and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. The Routhian, like the Hamiltonian, can be obtained from a Legendre transform of the Lagrangian, and has a similar mathematical form to the Hamiltonian, but is not exactly the same. The difference between the Lagrangian, Hamiltonian, and Routhian functions are their variables
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Space
Space
Space
is the boundless three-dimensional extent in which objects and events have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates
Socrates
in his reflections on what the Greeks called khôra (i.e
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Speed
In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity.[1] The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval;[2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed
Speed
has the dimensions of distance divided by time. The SI unit
SI unit
of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour
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Torque
Torque, moment, or moment of force is rotational force.[1] Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The symbol for torque is typically τ displaystyle tau , the lowercase Greek letter tau. When it is called moment of force, it is commonly denoted by M. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector[2] connecting the origin to the point of force application, and the angle between the force and lever arm vectors
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion (e.g. 7001600000000000000♠60 km/h to the north). Velocity
Velocity
is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity
Velocity
is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector
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Virtual Work
Virtual work
Virtual work
arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action
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Newton's Laws Of Motion
Newton's laws of motion
Newton's laws of motion
are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries,[1] and can be summarised as follows:First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.[2][3]Second law: In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma
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Analytical Mechanics
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics
Newtonian mechanics
considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws
Newton's laws
and Euler's laws is vectorial mechanics. By contrast, analytical mechanics uses scalar properties of motion representing the system as a whole—usually its total kinetic energy and potential energy—not Newton's vectorial forces of individual particles.[1] A scalar is a quantity, whereas a vector is represented by quantity and direction
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Lagrangian Mechanics
Lagrangian mechanics
Lagrangian mechanics
is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange
Joseph-Louis Lagrange
in 1788. In Lagrangian mechanics, the trajectory of
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Hamiltonian Mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics. It uses a different mathematical formalism, providing a more abstract understanding of the theory
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Appell's Equation Of Motion
In classical mechanics, Appell's equation of motion (aka Gibbs-Appell equation of motion) is an alternative general formulation of classical mechanics described by Paul Émile Appell
Paul Émile Appell
in 1900[1] and Josiah Willard Gibbs in 1879[2] Q r = ∂ S
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Hamilton–Jacobi Equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation. It is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi. In physics, the Hamilton-Jacobi equation is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion[citation needed], Lagrangian mechanics
Lagrangian mechanics
and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely. The HJE is also the only formulation of mechanics in which the motion of a particle can be represented as a wave
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Moment (physics)
In physics, a moment is an expression involving the product of a distance and a physical quantity, and in this way it accounts for how the physical quantity is located or arranged. Moments are usually defined with respect to a fixed reference point; they deal with physical quantities as measured at some distance from that reference point. For example, the moment of force acting on an object, often called torque, is the product of the force and the distance from a reference point. In principle, any physical quantity can be multiplied by distance to produce a moment; commonly used quantities include forces, masses, and electric charge distributions.Contents1 History 2 Elaboration2.1 Examples3 Multipole moments 4 Applications of multipole moments 5 See also 6 References 7 External linksHistory[edit] The concept of moment in physics is derived from the mathematical concept of moments.[1] [clarification needed]
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