Dynamics (mechanics)

Short description: Branch of physics studying forces and their effect on motion

Part of a series on

Classical mechanics
F=ddt(mv)

Second law of motion

* History
* Timeline
* Textbooks

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
* Inertial 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
* Koopman–von Neumann mechanics

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
* Coriolis force
* Pendulum
* Tangential speed
* Rotational speed

* Angular acceleration / displacement / frequency / velocity

Categories

Classical mechanics

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Dynamics is the branch of classical mechanics that is concerned with the study of forces and their effects on motion. Isaac Newton was the first to formulate the fundamental physical laws that govern dynamics in classical non-relativistic physics, especially his second law of motion.

## Contents

* 1 Principles
* 2 Linear and rotational dynamics
* 3 Force
* 4 Newton's laws
* 5 See also
* 6 References
* 7 Further reading

## 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, Maxwell's equations describe the kinematics. 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: Physics: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: Physics: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:

1. First law: If there is no net force on an object, then its velocity is constant: either the object is at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.[2][3]
2. Second law: The rate of change of linear momentum P of an object is equal to the net force Fnet, i.e., dP/dt = Fnet.
3. 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.

## See also

* Statics
* Multibody dynamics
* Rigid body dynamics
* Analytical dynamics

## References

1. ↑ "Force in Physics" (Physics tutorial). 2005. http://www.staff.amu.edu.pl/~romangoc/M3-1-force-physics.html.
2. ↑ (Series: Schaum's Outline Series) Schaum's outline of theory and problems of physics for engineering and science. New York: McGraw-Hill. 1999. pp. 58. ISBN 978-0-07-008498-8. https://archive.org/details/schaumsoutlineof00brow. "Newton's first law of motion."
3. ↑ Physics for Dummies. Hoboken: Wiley. 2005. pp. 64. ISBN 978-0-7645-5433-9. https://archive.org/details/physicsfordummie00holz. "Newton's laws of motion"

## Further reading

* A pocket-sized introduction to dynamics. Kingston upon Hull: University of Hull. 2008. doi:10.5281/zenodo.7504154. ISBN 978-90-812588-3-8. https://hal.archives-ouvertes.fr/hal-03188303/document.
* Swagatam (25 March 2010). "Calculating Engineering Dynamics Using Newton's Laws". Bright Hub. http://www.brighthub.com/engineering/mechanical/articles/111610.aspx.
* Kinematics and dynamics of machinery. London: Pearson. 2003. ISBN 978-0-201-35099-9.
* Dynamics of Machinery: Theory and Applications. Heidelberg: Springer. 2010. ISBN 978-3-540-89939-6.

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Sir Isaac Newton

Publications|

* Fluxions (1671)
* De Motu (1684)
* Principia (1687; writing)
* Opticks (1704)
* Queries (1704)
* Arithmetica (1707)
* De Analysi (1711)

Other writings|

* Quaestiones (1661–65)
* "standing on the shoulders of giants" (1675)
* Notes on the Jewish Temple (c. 1680)
* "General Scholium" (1713; "hypotheses non fingo" )
* Ancient Kingdoms Amended (1728)
* Corruptions of Scripture (1754)

Contributions|

* Calculus
* fluxion
* Impact depth
* Inertia
* Newton disc
* Newton polygon
* Newton–Okounkov body
* Newton's reflector
* Newtonian telescope
* Newton scale
* Newton's metal
* Newton's cradle
* Spectrum
* Structural coloration

Newtonianism|

* Bucket argument
* Newton's inequalities
* Newton's law of cooling
* Newton's law of universal gravitation
* post-Newtonian expansion
* parameterized
* gravitational constant
* Newton–Cartan theory
* Schrödinger–Newton equation
* Newton's laws of motion
* Kepler's laws
* Newtonian dynamics
* Newton's method in optimization
* Apollonius's problem
* truncated Newton method
* Gauss–Newton algorithm
* 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
* Newton's notation
* Rotating spheres
* Newton's cannonball
* Newton–Cotes formulas
* Newton's method
* generalized Gauss–Newton method
* Newton fractal
* Newton's identities
* Newton polynomial
* Newton's theorem of revolving orbits
* Newton–Euler equations
* Newton number
* kissing number problem
* Newton's quotient
* Parallelogram of force
* Newton–Puiseux theorem
* Absolute space and time
* Luminiferous aether
* Newtonian series
* table

Personal life|

* Woolsthorpe Manor (birthplace)
* Cranbury Park (home)
* Early life
* Later life
* Religious views
* Occult studies
* Scientific Revolution
* Copernican Revolution

Relations|

* Catherine Barton (niece)
* John Conduitt (nephew-in-law)
* Isaac Barrow (professor)
* William Clarke (mentor)
* Benjamin Pulleyn (tutor)
* John Keill (disciple)
* William Stukeley (friend)
* William Jones (friend)
* Abraham de Moivre (friend)

Depictions|

* Newton by Blake (monotype)
* Newton by Paolozzi (sculpture)

Namesake|

* Isaac Newton Institute
* Isaac Newton Medal
* Isaac Newton Telescope
* Isaac Newton Group of Telescopes
* Newton (unit)

Categories|

Category Isaac Newton not found

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