- Analytical dynamics
In

classical mechanics ,**analytical dynamics**, or more briefly**dynamics**, is concerned about the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies (particularlymass andmoment of inertia ). The foundation of modern day dynamics is Newtonian mechanics and its reformulation asLagrangian mechanics andHamiltonian mechanics .cite book |title=Geometric Algebra for Physicists |author=Chris Doran, Anthony N. Lasenby |publisher=Cambridge University Press |page= p. 54 |url=http://books.google.com/books?id=VW4yt0WHdjoC&pg=PA54&dq=classical+dynamics+-quantum+date:2002-2009&lr=&as_brr=0&sig=ACfU3U11syztEgIW0cnsvMxQhO1nQ51KRw

isbn=0521480221 |year=2003 ] cite book |title=The variational principles of mechanics |author=Cornelius Lanczos |url=http://books.google.com/books?id=ZWoYYr8wk2IC&pg=PR4&dq=isbn:0486650677&sig=ACfU3U2R5sLjGS22S-h8Z_j9RiPJnKcKZg#PPA5,M1 |edition=Reprint of 4th Edition of 1970 |publisher=Dover Publications Inc. |page=pp. 5-6 |isbn=0-486-65067-7 |year=1986] The field has a long and important history, as remarked by Hamilton:Quotation

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 byGalileo , and especially since the wonderful extension which was given to that science by Newton

William Rowan Hamilton, 1834 (Transcribed in "Classical Mechanics" by J.R. Taylor, p. 237)Some authors (for example, Taylor (2005) and Greenwood (1997)cite book |title=Classical Mechanics |author = Donald T Greenwood |page=p. 1 |url=http://books.google.com/books?id=x7rj83I98yMC&printsec=frontcover&dq=classical+dynamics&lr=&as_brr=0&sig=ACfU3U2-b1lzGZZqchuPz0_7Pu7IF-5UyQ#PPA1,M1 |isbn=0486696901 |publisher=Courier Dover Publications |year=1997 |edition=Reprint of 1977 edition] ) 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" (the study of motion and its relation to forces)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=p. 85 |url=http://books.google.com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&as_brr=0#PPA85,M1] and "kinematics " (dealing with the implications of observed motions without regard for circumstances causing them).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=0521358833 |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/books?id=epH1hCB7N2MC&printsec=frontcover&dq=inauthor:%22E+T+Whittaker%22&lr=&as_brr=0&sig=SN7_oYmNYM4QRSgjULXBU5jeQrA&source=gbs_book_other_versions_r&cad=0_2#PPA1,M1 ] 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 forcescite book |title=An Elementary Treatise on Kinematics and Dynamics |author=James Gordon MacGregor |page=p. "v" |publisher=Macmillan |url= http://books.google.com/books?id=3yMQAAAAYAAJ&printsec=frontcover&dq=kinematics+dynamics&lr=&as_brr=0#PPR5,M1 |year=1887 ] ; another approach separated statics, and combined kinetics and kinematics under the rubric dynamics.] cite book |title=Engineering mechanics |author=Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar |publisher=PHI Learning Pvt. Ltd. |year=2004 |isbn=8120321898 |page=p. "vi" |url=http://books.google.com/books?id=F7gaa1ShPKIC&printsec=frontcover&dq=statics+dynamics&lr=&as_brr=0&sig=ACfU3U2haQ0TLc90YwYiTtuhvIgfA6ZXEQ#PPR6,M1 ] This approach is common in engineering books on mechanics.**Diminishing emphasis**Today, "dynamics" and "kinematics" continue to be considered the two pillars of classical mechanics. 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" .cite book

author=John Robert Taylor

title=Classical Mechanics

publisher=University Science Books

url=http://books.google.com/books?id=P1kCtNr-pJsC&q=dynamics#search

isbn=189138922X, 9781891389221

year=2005] ] cite book

author=R. Douglas Gregory

title=Classical Mechanics: An Undergraduate Text

publisher=Cambridge University Press

url=http://books.google.com/books?id=uAfUQmQbzOkC&q=dynamics#search

isbn=0521826780, 9780521826785

year=2006] citation

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/books?id=LmAV8q_OOOgC

isbn=0750628960, 9780750628969

date=1976 ] cite book

author=Jorge Valenzuela José, Eugene Jerome Saletan

title=Classical Dynamics: A Contemporary Approach

publisher=Cambridge University Press

url=http://books.google.com/books?id=ZW0L5Xe9zhwC

isbn=0521636361, 9780521636360

year=1998 ] cite book

author=T. W. B. Kibble, Frank H. Berkshire

title=Classical Mechanics

publisher=Imperial College Press

url=http://books.google.com/books?id=0a8dk0eDxgEC

isbn=1860944353, 9781860944352

year=2004 ] cite book

author=Walter Greiner, S. Allan Bromley

title=Classical Mechanics: Point Particles and Relativity

publisher=Springer

url=http://books.google.com/books?id=L_APSPGoI5sC

isbn=0387955860, 9780387955865

year=2003 ] cite book

author=Gerald Jay Sussman, Jack Wisdom Meinhard, Edwin Mayer

title=Structure and Interpretation of Classical Mechanics

publisher=MIT Press

isbn=0262194554, 9780262194556

url=http://books.google.com/books?client=firefox-a&id=H_6Ux04cPv8C&q=dynamics#search

year= 2001] cite book

author=Harald Iro

title=A Modern Approach to Classical Mechanics

publisher=World Scientific

isbn=9812382135, 9789812382139

url=http://books.google.com/books?id=-L5ckgdxA5YC

year= 2002] 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 ".citation

title=The Feynman Lectures on Physics

first=RP | last=Feynman | first2=RB | last2=Leighton | first3=M | last3=Sands

author-link=Richard Feynman

isbn=0738209309

publisher=Perseus Books Group

year=2003

edition= Reprint of 1963 lectures

volume = Vol. 1 | page=Ch. 9 "Newton's Laws of Dynamics" ]**Related engineering branches*** Particle dynamics

*Rigid body dynamics

*Soft body dynamics

*Fluid dynamics

**Hydrodynamics

**Gas dynamics

**Aerodynamics **Related subjects***

Statics **References**

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