Editing Kinematics (section)

== Overview ==

'''Kinematics''' is a subfield of [[physics]] and [[mathematics]], developed in [[classical mechanics]], that describes the [[motion]] of points, [[Physical object|bodies]] (objects), and systems of bodies (groups of objects) without considering the [[force]]s that cause them to move.<ref name="Whittaker">{{cite book |title=[[A Treatise on the Analytical Dynamics of Particles and Rigid Bodies]]|author=Edmund Taylor Whittaker|author-link=E. T. Whittaker |at=Chapter 1 |year=1904 |publisher=Cambridge University Press |isbn=0-521-35883-3}}</ref><ref name=Beggs>{{cite book |title=Kinematics |author=Joseph Stiles Beggs |page=1 |url=https://books.google.com/books?id=y6iJ1NIYSmgC |isbn=0-89116-355-7 |year=1983 |publisher=Taylor & Francis}}</ref><ref name=Wright>{{cite book |title=Elements of Mechanics Including Kinematics, Kinetics and Statics|author=Thomas Wallace Wright |url=https://books.google.com/books?id=-LwLAAAAYAAJ |at=Chapter 1 |year=1896 |publisher=E and FN Spon}}</ref> 
The study of how forces act on bodies falls within [[kinetics (physics)|''kinetics'']] or [[Dynamics (mechanics)|''dynamics'']] (including [[analytical dynamics]]), not kinematics.

Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of both applied and pure [[mathematics]] since it can be studied without considering the mass of a body or the forces acting upon it.<ref>{{cite book |title=Engineering Mechanics: Dynamics |author=Russell C. Hibbeler |chapter=Kinematics and kinetics of a particle |chapter-url=https://books.google.com/books?id=tOFRjXB-XvMC&pg=PA298 |page=298 |isbn=978-0-13-607791-6 |year=2009 |edition=12th |publisher=Prentice Hall}}</ref><ref>{{cite book |title=Dynamics of Multibody Systems |author=Ahmed A. Shabana |chapter=Reference kinematics |chapter-url=https://books.google.com/books?id=zxuG-l7J5rgC&pg=PA28 |edition=2nd |publisher=Cambridge University Press |year=2003 |isbn=978-0-521-54411-5}}</ref><ref>{{cite book |title=Mechanical Systems, Classical Models: Particle Mechanics |chapter=Kinematics |page=287 |chapter-url=https://books.google.com/books?id=k4H2AjWh9qQC&pg=PA287 |author=P. P. Teodorescu |isbn=978-1-4020-5441-9 |year=2007 |publisher=Springer}}.</ref> A kinematics problem begins by describing the geometry of the system and declaring the [[initial conditions]] of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined.

Another way to describe kinematics is as the specification of the possible states of a physical system. Dynamics then describes the evolution of a system through such states. [[Robert Spekkens]] argues that this division cannot be empirically tests and thus has no physical basis.<ref>{{Cite book |last=Spekkens |first=Robert W. |chapter=The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure |series=The Frontiers Collection |date=2015 |editor-last=Aguirre |editor-first=Anthony |editor2-last=Foster |editor2-first=Brendan |editor3-last=Merali |editor3-first=Zeeya |title=Questioning the Foundations of Physics |chapter-url=https://link.springer.com/10.1007/978-3-319-13045-3_2 |language=en |location=Cham |publisher=Springer International Publishing |pages=5–16 |doi=10.1007/978-3-319-13045-3_2 |isbn=978-3-319-13044-6}}</ref>

Kinematics is used in [[astrophysics]] to describe the motion of [[celestial bodies]] and collections of such bodies. In [[mechanical engineering]], [[robotics]], and [[biomechanics]],<ref name="Biewener">{{cite book |title=Animal Locomotion |url=https://books.google.com/books?id=yMaN9pk8QJAC |author=A. Biewener |isbn=019850022X |publisher=Oxford University Press |year=2003}}</ref> kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an [[engine]], a [[robot kinematics|robotic arm]] or the [[human skeleton]].

[[Geometric transformation]]s, including called [[rigid transformation]]s, are used to describe the movement of components in a [[mechanical system]], simplifying the derivation of the equations of motion. They are also central to [[Lagrangian mechanics|dynamic analysis]].

[[Robot kinematics|Kinematic analysis]] is the process of measuring the kinematic [[Physical quantity|quantities]] used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given [[Mechanism (engineering)|mechanism]] and, working in reverse, using [[Burmester theory|kinematic synthesis]] to design a mechanism for a desired range of motion.<ref name="McCarthy2010">J. M. McCarthy and G. S. Soh, 2010, [https://books.google.com/books?id=jv9mQyjRIw4C&pg=PA231 ''Geometric Design of Linkages,''] Springer, New York.</ref> <!-- I am sure that these are the best examples: The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed [[four-bar linkage]]. --> In addition, kinematics applies [[algebraic geometry]] to the study of the [[mechanical advantage]] of a [[mechanical system]] or mechanism.

[[Relativistic mechanics#Relativistic kinematics|Relativistic_kinematics]] applies the [[special theory of relativity]] to the geometry of object motion. The topics include [[time dilation]], [[length contraction]] and the [[Lorentz transformation]].<ref>{{Cite book |last1=Kleppner |first1=Daniel |url=https://www.cambridge.org/core/product/identifier/9781139013963/type/book |title=An Introduction to Mechanics |last2=Kolenkow |first2=Robert |date=2013-11-18 |publisher=Cambridge University Press |isbn=978-0-521-19811-0 |edition=2 |doi=10.1017/cbo9781139013963}}</ref>{{rp|loc=12.8}} The kinematics of relativity operates in a [[spacetime]] geometry where spatial points are augmented with a time coordinate to form [[four-vectors|4-vectors]].<ref>{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1st |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|221}}

[[Werner Heisenberg]] reinterpreted classical kinetics for quantum systems in his 1925 paper [[Umdeutung paper|"On the quantum-theoretical reinterpretation of kinematical and mechanical relationships"]].<ref>Heisenberg, Werner. "Quantum-theoretical re-interpretation of kinematic and mechanical relations." Z. Phys 33 (1925): 879-893.</ref> Dirac noted the similarity in structure between Heisenberg's formulations and classical [[Poisson brackets]].<ref>{{Cite book |last1=Mehra |first1=J |title=The Historical Development of Quantum Theory. |last2=Rechenberg |first2=H |publisher=Springer |year=2000}}</ref>{{rp|143}} In a follow up paper in 1927 Heisenberg showed that classical kinematic notions like velocity and energy are valid in quantum mechanics, but pairs of conjugate kinematic and dynamic quantities cannot be simultaneously measure, a  result he called indeterminacy but which became known as the [[uncertainty principle]].<ref>{{Cite book |last=Heisenberg |first=Werner |title=Quantum Theory and Measurement |date=1983 |publisher=Princeton University Press |isbn=978-1-4008-5455-4 |editor-last=Wheeler |editor-first=John Archibald |series=Princeton series in physics |location=Princeton, New Jersey |chapter=The Physical Content of Quantum Kinematics and Mechanics |editor-last2=Zurek |editor-first2=Wojciech Hubert}}</ref>