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Classical mechanics - Wikipedia, the free encyclopedia Page 1 of 13 Classical mechanics From Wikipedia, the free encyclopedia (Redirected from Newtonian mechanics) In physics, classical mechanics is one of the two major Classical mechanics sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the Newton's Second Law action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of History of classical mechanics · the oldest and largest subjects in science, engineering and Timeline of classical mechanics technology. Branches Classical mechanics describes the motion of macroscopic Statics · Dynamics / Kinetics · Kinematics · objects, from projectiles to parts of machinery, as well as Applied mechanics · Celestial mechanics · astronomical objects, such as spacecraft, planets, stars, and Continuum mechanics · galaxies. Besides this, many specializations within the Statistical mechanics subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely Formulations accurate results as long as the domain of study is restricted Newtonian mechanics (Vectorial to large objects and the speeds involved do not approach mechanics) the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to Analytical mechanics: introduce the other major sub-field of mechanics, quantum Lagrangian mechanics mechanics, which reconciles the macroscopic laws of Hamiltonian mechanics physics with the atomic nature of matter and handles the Fundamental concepts wave-particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, Space · Time · Velocity · Speed · Mass · classical mechanics is enhanced by special relativity. Acceleration · Gravity · Force · Impulse · General relativity unifies special relativity with Newton's Torque / Moment / Couple · Momentum · law of universal gravitation, allowing physicists to handle Angular momentum · Inertia · gravitation at a deeper level. Moment of inertia · Reference frame · The term classical mechanics was coined in the early 20th Energy · Kinetic energy · Potential energy · century to describe the system of physics begun by Isaac Mechanical work · Virtual work · Newton and many contemporary 17th century natural D'Alembert's principle philosophers, building upon the earlier astronomical theories of Johannes Kepler, which in turn were based on Core topics the precise observations of Tycho Brahe and the studies of Rigid body · Rigid body dynamics · terrestrial projectile motion of Galileo. Because these Euler's equations (rigid body dynamics) · aspects of physics were developed long before the emergence of quantum physics and relativity, some sources Motion · Newton's laws of motion · exclude Einstein's theory of relativity from this category. Newton's law of universal gravitation · However, a number of modern sources do include Equations of motion · relativistic mechanics, which in their view represents Inertial frame of reference · classical mechanics in its most developed and most Non-inertial reference frame · [note 1] accurate form. Rotating reference frame · Fictitious force · The initial stage in the development of classical mechanics Linear motion · is often referred to as Newtonian mechanics, and is Mechanics of planar particle motion · associated with the physical concepts employed by and the Displacement (vector) · Relative velocity · http://en.wikipedia.org/wiki/Newtonian_mechanics 5/23/2011 Classical mechanics - Wikipedia, the free encyclopedia Page 2 of 13 mathematical methods invented by Newton himself, in parallel with Leibniz, and others. This is further described Friction · Simple harmonic motion · in the following sections. Later, more abstract and general Harmonic oscillator · Vibration · Damping · methods were developed, leading to reformulations of Damping ratio · Rotational motion · classical mechanics known as Lagrangian mechanics and Circular motion · Uniform circular motion · Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend Non-uniform circular motion · substantially beyond Newton's work, particularly through Centripetal force · Centrifugal force · their use of analytical mechanics. Ultimately, the Centrifugal force (rotating reference frame) · mathematics developed for these were central to the Reactive centrifugal force · Coriolis force · creation of quantum mechanics. Pendulum · Rotational speed · Angular acceleration · Angular velocity · Contents Angular frequency · Angular displacement Scientists 1 Description of the theory 1.1 Position and its derivatives Galileo Galilei · Isaac Newton · 1.1.1 Velocity and speed Jeremiah Horrocks · Leonhard Euler · 1.1.2 Acceleration Jean le Rond d'Alembert · Alexis Clairaut · 1.1.3 Frames of reference Joseph Louis Lagrange · 1.2 Forces; Newton's second law Pierre-Simon Laplace · 1.3 Work and energy William Rowan Hamilton · 1.4 Beyond Newton's Laws Siméon-Denis Poisson 2 History 3 Limits of validity 3.1 The Newtonian approximation to special relativity 3.2 The classical approximation to quantum mechanics 4 Branches 5 See also 6 Notes 7 References 8 Further reading 9 External links Description of the theory The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn. In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as http://en.wikipedia.org/wiki/Newtonian_mechanics 5/23/2011 Classical mechanics - Wikipedia, the free encyclopedia Page 3 of 13 composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle. The analysis of projectile motion is a part of classical mechanics. Position and its derivatives Main article: Kinematics The position of a point particle is defined with respect The SI derived "mechanical" to an arbitrary fixed reference point, O, in space, (that is, not electromagnetic or thermal) usually accompanied by a coordinate system, with the units with kg, m and s reference point located at the origin of the coordinate Position m system. It is defined as the vector r from O to the particle. In general, the point particle need not be Angular position/Angle unitless (radian) stationary relative to O, so r is a function of t, the time velocity m s −1 elapsed since an arbitrary initial time. In pre-Einstein −1 relativity (known as Galilean relativity), time is Angular velocity s considered an absolute, i.e., the time interval between acceleration m s −2 any given pair of events is the same for all observers. In addition to relying on absolute time, classical Angular acceleration s−2 mechanics assumes Euclidean geometry for the jerk m s −3 structure of space. [1] "Angular jerk" s−3 Velocity and speed specific energy m2 s −2 Main articles: Velocity and speed absorbed dose rate m2 s −3 2 The velocity , or the rate of change of position with moment of inertia kg m time, is defined as the derivative of the position with momentum kg m s −1 respect to time or 2 −1 angular momentum kg m s −2 . force kg m s torque kg m 2 s −2 In classical mechanics, velocities are directly additive energy kg m 2 s −2 and subtractive. For example, if one car traveling East http://en.wikipedia.org/wiki/Newtonian_mechanics 5/23/2011 Classical mechanics - Wikipedia, the free encyclopedia Page 4 of 13 at 60 km/h passes another car traveling East at 50 km/h, power kg m 2 s −3 then from the perspective of the slower car, the faster car is traveling east at 60 − 50 = 10 km/h. Whereas, pressure and energy density kg m −1 s −2 from the perspective of the faster car, the slower car is −2 moving 10 km/h to the West. Velocities are directly surface tension kg s additive as vector quantities ; they must be dealt with Spring constant kg s −2 using vector analysis. irradiance and energy flux kg s −3 Mathematically, if the velocity of the first object in the kinematic viscosity 2 −1 previous discussion is denoted by the vector u = ud and m s the velocity of the second object by the vector v = ve, dynamic viscosity kg m −1 s −1 where u is the speed of the first object, v is the speed of −3 the second object, and d and e are unit vectors in the Density(mass density) kg m directions of motion of each particle respectively, then Density(weight density) kg m −2 s −2 the velocity of the first object as seen by the second object is Number density m−3 Action 2 −1 kg m s Similarly, When both objects are moving in the same direction, this equation can be simplified to Or, by ignoring direction, the difference can be given in terms of speed only: Acceleration Main article: Acceleration The acceleration , or rate of change of velocity, is the derivative of the velocity with respect
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