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Analytical mechanics

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+#REDIRECT [[Analytical mechanics]]
-{{Merge to |Dynamics (physics)|discuss=Talk:Dynamics (physics)#Merger Analytical dynamics and Dynamics |date=May 2010}}
-{{for|dynamics as the time evolution of physical processes|Dynamics (physics)}}
-{{Classical mechanics|cTopic=Branches}}
-In [[classical mechanics]], '''analytical dynamics''', or more briefly '''dynamics''', is concerned about the relationship between [[Motion (physics)|motion]] of bodies and its causes, namely the [[force (physics)|force]]s acting on the bodies and the properties of the bodies (particularly [[mass]] and [[moment of inertia]]).   The foundation of modern day dynamics is [[Classical mechanics|Newtonian mechanics]] and its reformulation as [[Lagrangian mechanics]] and [[Hamiltonian mechanics]].<ref name=Doran>{{cite book |title=Geometric Algebra for Physicists |author=Chris Doran, Anthony N. Lasenby | publisher=Cambridge University Press | page= 54 | url=http://books.google.com/?id=VW4yt0WHdjoC&pg=PA54&dq=classical+dynamics+-quantum+date:2002-2009| isbn=0-521-48022-1| year=2003 }}</ref><ref name=Lanczos>{{cite book |title=The variational principles of mechanics |author=Cornelius Lanczos |url=http://books.google.com/?id=ZWoYYr8wk2IC&pg=PR4&dq=isbn=0486650677 |edition=Reprint of 4th Edition of 1970 |publisher=Dover Publications Inc. |pages=5–6 |isbn=0-486-65067-7 |year=1986}}</ref>
-==History==
-The field has a long and important history, as remarked by [[William Rowan Hamilton|Hamilton]]:
-"The theoretical development of the laws of motion of bodies is a problem of such interest and importance that it has engaged the attention of all the eminent mathematicians since the invention of the dynamics as a mathematical science by [[Galileo]], and especially since the wonderful extension which was given to that science by [[Isaac Newton|Newton]]."  William Rowan Hamilton, 1834 (Transcribed in ''Classical Mechanics'' by J.R. Taylor, p. 237<ref name="Taylor" />)
-Some authors (for example, Taylor (2005)<ref name="Taylor" /> and Greenwood (1997)<ref name=Greenwood>
-{{cite book |title=Classical Mechanics |author = Donald T Greenwood |page=1 |url=http://books.google.com/?id=x7rj83I98yMC&printsec=frontcover&dq=classical+dynamics |isbn=0-486-69690-1 |publisher=Courier Dover Publications |year=1997 |edition=Reprint of 1977}}</ref>) include [[special relativity]] within classical dynamics.
-==Relationship to statics, kinetics, and kinematics==
-Historically, there were three branches of [[classical mechanics]]:
-*"[[statics]]" (the study of equilibrium and its relation to forces)
-*"[[Kinetics (physics)|kinetics]]" (the study of motion and its relation to forces),<ref name=Wright>{{cite book |title=Elements of Mechanics Including Kinematics, Kinetics and Statics: with applications |year=1896 |publisher=E. and F. N. Spon |author=Thomas Wallace Wright |page=85 |url=http://books.google.com/?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics}}</ref> and
-*"[[kinematics]]" (dealing with the implications of observed motions without regard for circumstances causing them).<ref name=Whittaker1>
-{{cite book |title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies |author=Edmund Taylor Whittaker |isbn=0-521-35883-3 |publisher=Cambridge University Press |page=Chapter 1, p. 1 |year=1988 |edition=Fourth edition of 1936 with foreword by Sir William McCrea |url=http://books.google.com/?id=epH1hCB7N2MC&printsec=frontcover&dq=inauthor:%22E+T+Whittaker%22 }}</ref>
-These three subjects have been connected to ''dynamics'' in several ways. One approach combined statics and kinetics under the name dynamics, which became the branch dealing with determination of the motion of bodies resulting from the action of specified forces;<ref name=MacGregor>{{cite book |title=An Elementary Treatise on Kinematics and Dynamics |author=James Gordon MacGregor |page=''v'' |publisher=Macmillan |url=  http://books.google.com/?id=3yMQAAAAYAAJ&printsec=frontcover&dq=kinematics+dynamics |year=1887 }}</ref> another approach separated statics, and combined kinetics and kinematics under the rubric dynamics.<ref name=Timoshenko>
-{{cite book |title=Engineering mechanics| year=1956| publisher= McGraw Hill| author=  Stephen Timoshenko, Donovan Harold Young| url=http://books.google.com/?id=I548AAAAIAAJ&q=engineering+mechanics+inauthor:Timoshenko&dq=engineering+mechanics+inauthor:Timoshenko}}
-</ref><ref name=Rao1>{{cite book |title=Engineering mechanics |author=Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar |publisher=PHI Learning Pvt. Ltd. |year=2004 |isbn=81-203-2189-8 |page=''vi'' |url=http://books.google.com/?id=F7gaa1ShPKIC&printsec=frontcover&dq=statics+dynamics  }}</ref> This approach is common in engineering books on mechanics, and is still in widespread use among mechanicians.
-===Fundamental importance in engineering, diminishing emphasis in physics===
-Today, ''dynamics'' and ''kinematics'' continue to be considered the two pillars of classical mechanics.  Dynamics is still included in mechanical, aerospace, and other engineering curricula because of its importance in machine design, the design of land, sea, air and space vehicles and other applications. However, few modern physicists concern themselves with an independent treatment of "dynamics" or "kinematics," nevermind "statics" or "kinetics."  Instead, the entire undifferentiated subject is referred to as ''classical mechanics''.  In fact, many undergraduate and graduate text books since mid-20th century on "classical mechanics" lack chapters titled "dynamics" or "kinematics."<ref name="Taylor">{{cite book| author=John Robert Taylor| title=Classical Mechanics|  publisher=University Science Books| url=http://books.google.com/?id=P1kCtNr-pJsC&q=dynamics#search| isbn=978-1-891389-22-1| year=2005}}</ref><ref name=Hestenes>{{cite book |author=David Hestenes |authorlink=David Hestenes |title=New Foundations for Classical Mechanics |publisher=Springer |page=198 |url=http://books.google.com/?id=eU2qm8wavRwC&pg=PA198&dq=dynamics+kinematics |isbn=0-7923-5514-8 |year=1999 }}</ref><ref name="Gregory">{{cite book | author=R. Douglas Gregory| title=Classical Mechanics: An Undergraduate Text|  publisher=Cambridge University Press| url=http://books.google.com/?id=uAfUQmQbzOkC&q=dynamics#search| isbn=978-0-521-82678-5| year=2006}}</ref><ref name="Landau et al.">{{Cite document| first=L. D. |last=Landau | first2=E. M. | last2=Lifshitz | first3=J.B. | last3=Sykes | first4=J. S. | last4=Bell| author-link=Lev Landau | author2-link=Evgeny Lifshitz| title=Mechanics| volume=1| publisher=Butterworth-Heinemann| url=http://books.google.com/?id=LmAV8q_OOOgC|  isbn=978-0-7506-2896-9| date=1976| postscript= }}</ref><ref name="Jose et al.">{{cite book| author=Jorge Valenzuela José, Eugene Jerome Saletan| title=Classical Dynamics: A Contemporary Approach| publisher=Cambridge University Press| url=http://books.google.com/?id=ZW0L5Xe9zhwC| isbn=978-0-7506-2896-9| year=1998 }}</ref><ref name="Kibble et al.">{{cite book| author=T. W. B. Kibble, Frank H. Berkshire| title=Classical Mechanics
-| publisher=Imperial College Press| url=http://books.google.com/?id=0a8dk0eDxgEC| isbn=978-1-86094-435-2| year=2004 }}</ref><ref name="Greiner et al.">{{cite book | author=Walter Greiner, S. Allan Bromley| title=Classical Mechanics: Point Particles and Relativity| publisher=Springer| url=http://books.google.com/?id=L_APSPGoI5sC| isbn=978-0-387-95586-5| year=2003}}</ref><ref name="Sussman">{{cite book| author=Gerald Jay Sussman, Jack Wisdom Meinhard, Edwin Mayer| title=Structure and Interpretation of Classical Mechanics| publisher=MIT Press| isbn=978-0-262-19455-6
-| url=http://books.google.com/?id=H_6Ux04cPv8C&q=dynamics#search| year= 2001}}</ref><ref name="Iro">{{cite book| author=Harald Iro| title=A Modern Approach to Classical Mechanics| publisher=World Scientific| isbn=978-981-238-213-9| url=http://books.google.com/?id=-L5ckgdxA5YC| year= 2002}</ref>
-In these books, although the word "dynamics" is used when acceleration is ascribed to a force, the word "kinetics" is never mentioned. However, clear exceptions exist. Prominent examples include ''[[The Feynman Lectures on Physics]]''.<ref name=Feynman>{{Cite book| title=The Feynman Lectures on Physics| first=RP | last=Feynman | first2=RB | last2=Leighton | first3=M | last3=Sands| author-link=Richard Feynman| isbn=0-7382-0930-9| publisher= Perseus Books Group| year=2003| edition= Reprint of 1963 lectures| volume = Vol. 1 | page=Ch. 9 ''Newton's Laws of Dynamics''| postscript= }}</ref>
-;List of Fundamental Dynamics Principles
-* [[Newton's laws of motion]]
-** [[Inertia]]
-** [[Acceleration]]
-** [[Momentum]]
-** [[Reaction (physics)|Reaction]]
-* [[Newton's law of universal gravitation]]
-* [[Special theory of relativity]]
-==Axioms and mathematical treatments==
-* [[Variational principle]]s and [[Joseph Louis Lagrange|Lagrange]]'s equations
-* [[William Rowan Hamilton|Hamilton]]'s equations
-* [[Canonical transformation]]s
-* [[Hamilton-Jacobi equation|Hamilton-Jacobi Theory]]
-==Related engineering branches==
-* Particle dynamics
-* [[Rigid body dynamics]]
-* [[Soft body dynamics]]
-* [[Fluid dynamics]]
-** [[Hydrodynamics]]
-** [[Gas dynamics]]
-** [[Aerodynamics]]
-===Related subjects===
-* [[Statics]]
-==References==
-{{Reflist|2}}
-[[Category:Dynamics]]
-[[Category:Classical mechanics]]
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