Analytical dynamics


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 (particularly mass and moment of inertia). The foundation of modern day dynamics is Newtonian mechanics and its reformulation as Lagrangian mechanics and Hamiltonian 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 by Galileo, 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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