Dynamics (mechanics)

For dynamics as the mathematical analysis of the motion of bodies as a result of impressed forces, see analytical dynamics.

Classical mechanics
$\vec{F} = m\vec{a}$ Second law of motion
History Timeline
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation
Core topics Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive rotating reference frame Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity
Scientists Galileo Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy

Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.

Principles

Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion. However, all three laws of motion are taken into account because these are interrelated in any given observation or experiment.

Linear and rotational dynamics

The study of dynamics falls under two categories: linear and rotational. Linear dynamics pertains to objects moving in a line and involves such quantities as force, mass/inertia, displacement (in units of distance), velocity (distance per unit time), acceleration (distance per unit of time squared) and momentum (mass times unit of velocity). Rotational dynamics pertains to objects that are rotating or moving in a curved path and involves such quantities as torque, moment of inertia/rotational inertia, angular displacement (in radians or less often, degrees), angular velocity (radians per unit time), angular acceleration (radians per unit of time squared) and angular momentum (moment of inertia times unit of angular velocity). Very often, objects exhibit linear and rotational motion.

For classical electromagnetism, it is Maxwell's equations that describe the dynamics. And the dynamics of classical systems involving both mechanics and electromagnetism are described by the combination of Newton's laws, Maxwell's equations, and the Lorentz force.

Force

Main article: Force

From Newton, force can be defined as an exertion or pressure which can cause an object to accelerate. The concept of force is used to describe an influence which causes a free body (object) to accelerate. It can be a push or a pull, which causes an object to change direction, have new velocity, or to deform temporarily or permanently. Generally speaking, force causes an object's state of motion to change.^[1]

Newton's laws

Main article: Newton's laws of motion

Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows:

First law: If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.^[2]^[3]
Second law: The rate of change of linear momentum P of an object is equal to the net force F_net, i.e., dP/dt = F_net.
Third law: When a first body exerts a force F₁ on a second body, the second body simultaneously exerts a force F₂ = −F₁ on the first body. This means that F₁ and F₂ are equal in magnitude and opposite in direction.

Newton's Laws of Motion are valid only in an inertial frame of reference

References

Wikibooks has a book on the topic of: School of Engineering/Dynamics

Wikiversity has learning materials about Topic:Dynamics

↑ Goc, Roman (2004-2005 copyright date). "Force in Physics" (Physics tutorial). Retrieved 2010-02-18. Check date values in: |date= (help)
↑ Browne, Michael E. (July 1999). Schaum's outline of theory and problems of physics for engineering and science (Series: Schaum's Outline Series). McGraw-Hill Companies. p. 58. ISBN 978-0-07-008498-8.
↑ Holzner, Steven (December 2005). Physics for Dummies. Wiley, John & Sons, Incorporated. p. 64. ISBN 978-0-7645-5433-9.

Swagatam (25 March 011). "Calculating Engineering Dynamics Using Newton's Laws". Bright Hub. Retrieved 2010-04-10. Check date values in: |date= (help)
Wilson, C. E. (2003). Kinematics and dynamics of machinery. Pearson Education. ISBN 978-0-201-35099-9.
Dresig, H.; Holzweißig, F. (2010). Dynamics of Machinery. Theory and Applications. Springer Science+Business Media, Dordrecht, London, New York. ISBN 978-3-540-89939-6.

Isaac Newton

Publications	De analysi per aequationes numero terminorum infinitas (1669, published 1711) Method of Fluxions (1671) De motu corporum in gyrum (1684) Philosophiæ Naturalis Principia Mathematica (1687) General Scholium (1713) Opticks (1704) The Queries (1704) Arithmetica Universalis (1707)

Other writings	Notes on the Jewish Temple Quaestiones quaedam philosophicae The Chronology of Ancient Kingdoms Amended (1728) An Historical Account of Two Notable Corruptions of Scripture (1754)

Newtonianism	Bucket argument Newton's inequalities Newton's law of cooling Newton's law of universal gravitation Post-Newtonian expansion Parameterized post-Newtonian formalism Newton–Cartan theory Schrödinger–Newton equation Gravitational constant Newton's laws of motion Newtonian dynamics Newton's method in optimization Gauss–Newton algorithm Truncated Newton method Newton's rings Newton's theorem about ovals Newton–Pepys problem Newtonian potential Newtonian fluid Classical mechanics Newtonian fluid Corpuscular theory of light Leibniz–Newton calculus controversy Rotating spheres Newton's cannonball Newton–Cotes formulas Newton's method Newton fractal Generalized Gauss–Newton method Newton's identities Newton polynomial Newton's theorem of revolving orbits Newton–Euler equations Newton number Kissing number problem Power number Solar mass Dynamics Absolute time and space Finite difference Table of Newtonian series Impact depth Structural coloration Inertia

Life	Cranbury Park Woolsthorpe Manor Early life of Isaac Newton Later life of Isaac Newton Religious views of Isaac Newton Isaac Newton's occult studies The Mysteryes of Nature and Art Scientific revolution Copernican Revolution

Friends and family	Catherine Barton John Conduitt William Clarke Benjamin Pulleyn William Stukeley William Jones Isaac Barrow Abraham de Moivre John Keill

Discoveries and inventions	Calculus Newton disc Newton polygon Newton–Okounkov body Newton's reflector Newtonian telescope Newton scale Newton's metal Newton's cradle Sextant

Phrases	Hypotheses non fingo Standing on the shoulders of giants

Theory expansions	Kepler's laws of planetary motion Problem of Apollonius

Related	Writing of Principia Mathematica Newton (Blake) List of things named after Isaac Newton Isaac Newton in popular culture Elements of the Philosophy of Newton Isaac Newton S/O Philipose Newton (unit)

Authority control	NDL: 00561691

This article is issued from Wikipedia - version of the Saturday, December 19, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.