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{{for|dynamics as the time evolution of physical processes|Dynamics (mechanics)}}
{{for|dynamics as the time evolution of physical processes|Dynamics (mechanics)}}
{{Classical mechanics|cTopic=Branches}}
{{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>
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=https://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=https://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==
==History==
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Some authors (for example, Taylor (2005)<ref name="Taylor" /> and Greenwood (1997)<ref name=Greenwood>
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.
{{cite book |title=Classical Mechanics |author = Donald T Greenwood |page=1 |url=https://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==
==Relationship to statics, kinetics, and kinematics==
Historically, there were three branches of [[classical mechanics]]:
Historically, there were three branches of [[classical mechanics]]:
*"[[statics]]" (the study of equilibrium and its relation to forces)
*"[[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
*"[[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=https://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>
*"[[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>
{{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=https://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>
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= https://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}}
{{cite book |title=Engineering mechanics| year=1956| publisher= McGraw Hill| author= Stephen Timoshenko, Donovan Harold Young| url=https://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.
</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=https://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===
===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=[[Tom Kibble|T. W. B. Kibble]], Frank H. Berkshire| title=[[Classical Mechanics (Kibble and Berkshire)|Classical Mechanics]]
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=https://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=https://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=https://books.google.com/?id=uAfUQmQbzOkC&q=dynamics#search| isbn=978-0-521-82678-5| year=2006}}</ref><ref name="Landau et al.">{{Cite journal| 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=https://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=https://books.google.com/?id=ZW0L5Xe9zhwC| isbn=978-0-7506-2896-9| year=1998 }}</ref><ref name="Kibble et al.">{{cite book| author=[[Tom Kibble|T. W. B. Kibble]], Frank H. Berkshire| title=[[Classical Mechanics (Kibble and Berkshire)|Classical Mechanics]]
| publisher=Imperial College Press| 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
| publisher=Imperial College Press| 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=https://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>
| url=https://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=https://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>
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>


Revision as of 22:57, 11 March 2016

For dynamics as the time evolution of physical processes, see Dynamics (mechanics).
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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.[1][2]

History

The field has a long and important history, as remarked by 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 Newton." William Rowan Hamilton, 1834 (Transcribed in Classical Mechanics by J.R. Taylor, p. 237[3])

Some authors (for example, Taylor (2005)[3] and Greenwood (1997)[4]) 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),[5] and
  • "kinematics" (dealing with the implications of observed motions without regard for circumstances causing them).[6]

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;[7] another approach separated statics, and combined kinetics and kinematics under the rubric dynamics.[8][9] 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."[3][10][11][12][13][14][15][16][17] 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.[18]

List of Fundamental Dynamics Principles

Axioms and mathematical treatments

References

  1. ^ Chris Doran, Anthony N. Lasenby (2003). Geometric Algebra for Physicists. Cambridge University Press. p. 54. ISBN 0-521-48022-1.
  2. ^ Cornelius Lanczos (1986). The variational principles of mechanics (Reprint of 4th Edition of 1970 ed.). Dover Publications Inc. pp. 5–6. ISBN 0-486-65067-7.
  3. ^ a b c John Robert Taylor (2005). Classical Mechanics. University Science Books. ISBN 978-1-891389-22-1.
  4. ^ Donald T Greenwood (1997). Classical Mechanics (Reprint of 1977 ed.). Courier Dover Publications. p. 1. ISBN 0-486-69690-1.
  5. ^ Thomas Wallace Wright (1896). Elements of Mechanics Including Kinematics, Kinetics and Statics: with applications. E. and F. N. Spon. p. 85.
  6. ^ Edmund Taylor Whittaker (1988). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies (Fourth edition of 1936 with foreword by Sir William McCrea ed.). Cambridge University Press. p. Chapter 1, p. 1. ISBN 0-521-35883-3.
  7. ^ James Gordon MacGregor (1887). An Elementary Treatise on Kinematics and Dynamics. Macmillan. p. v.
  8. ^ Stephen Timoshenko, Donovan Harold Young (1956). Engineering mechanics. McGraw Hill.
  9. ^ Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar (2004). Engineering mechanics. PHI Learning Pvt. Ltd. p. vi. ISBN 81-203-2189-8.{{cite book}}: CS1 maint: multiple names: authors list (link)
  10. ^ David Hestenes (1999). New Foundations for Classical Mechanics. Springer. p. 198. ISBN 0-7923-5514-8.
  11. ^ R. Douglas Gregory (2006). Classical Mechanics: An Undergraduate Text. Cambridge University Press. ISBN 978-0-521-82678-5.
  12. ^ Landau, L. D.; Lifshitz, E. M.; Sykes, J.B.; Bell, J. S. (1976). "Mechanics". 1. Butterworth-Heinemann. ISBN 978-0-7506-2896-9. {{cite journal}}: Cite journal requires |journal= (help)
  13. ^ Jorge Valenzuela José, Eugene Jerome Saletan (1998). Classical Dynamics: A Contemporary Approach. Cambridge University Press. ISBN 978-0-7506-2896-9.
  14. ^ T. W. B. Kibble, Frank H. Berkshire (2004). Classical Mechanics. Imperial College Press. ISBN 978-1-86094-435-2.
  15. ^ Walter Greiner, S. Allan Bromley (2003). Classical Mechanics: Point Particles and Relativity. Springer. ISBN 978-0-387-95586-5.
  16. ^ Gerald Jay Sussman, Jack Wisdom Meinhard, Edwin Mayer (2001). Structure and Interpretation of Classical Mechanics. MIT Press. ISBN 978-0-262-19455-6.{{cite book}}: CS1 maint: multiple names: authors list (link)
  17. ^ Harald Iro (2002). A Modern Approach to Classical Mechanics. World Scientific. ISBN 978-981-238-213-9.
  18. ^ Feynman, RP; Leighton, RB; Sands, M (2003). The Feynman Lectures on Physics. Vol. Vol. 1 (Reprint of 1963 lectures ed.). Perseus Books Group. p. Ch. 9 Newton's Laws of Dynamics. ISBN 0-7382-0930-9. {{cite book}}: |volume= has extra text (help)
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