Analytical dynamics

For dynamics as the time evolution of physical processes, see Dynamics (physics).
Classical mechanics
History of classical mechanics · Timeline of classical mechanics
Branches
Statics · Dynamics / Kinetics · Kinematics · Applied mechanics · Celestial mechanics · Continuum mechanics · Statistical mechanics

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] 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.

Contents

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 curriculums 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]

Fundamental Principles

Axioms and mathematical treatments

Related engineering branches

Related subjects

References

  1. ↑ Chris Doran, Anthony N. Lasenby (2003). Geometric Algebra for Physicists. Cambridge University Press. p. 54. ISBN 0521480221. http://books.google.com/books?id=VW4yt0WHdjoC&pg=PA54&dq=classical+dynamics+-quantum+date:2002-2009&lr=&as_brr=0&sig=ACfU3U11syztEgIW0cnsvMxQhO1nQ51KRw. 
  2. ↑ Cornelius Lanczos (1986). The variational principles of mechanics (Reprint of 4th Edition of 1970 ed.). Dover Publications Inc.. p. 5–6. ISBN 0-486-65067-7. http://books.google.com/books?id=ZWoYYr8wk2IC&pg=PR4&dq=isbn=0486650677&sig=ACfU3U2R5sLjGS22S-h8Z_j9RiPJnKcKZg#PPA5,M1. 
  3. ↑ 3.0 3.1 3.2 John Robert Taylor (2005). Classical Mechanics. University Science Books. ISBN 189138922X, 9781891389221. http://books.google.com/books?id=P1kCtNr-pJsC&q=dynamics#search. 
  4. ↑ Donald T Greenwood (1997). Classical Mechanics (Reprint of 1977 ed.). Courier Dover Publications. p. 1. ISBN 0486696901. http://books.google.com/books?id=x7rj83I98yMC&printsec=frontcover&dq=classical+dynamics&lr=&as_brr=0&sig=ACfU3U2-b1lzGZZqchuPz0_7Pu7IF-5UyQ#PPA1,M1. 
  5. ↑ Thomas Wallace Wright (1896). Elements of Mechanics Including Kinematics, Kinetics and Statics: with applications. E. and F. N. Spon. p. 85. http://books.google.com/books?id=-LwLAAAAYAAJ&printsec=frontcover&dq=mechanics+kinetics&lr=&as_brr=0#PPA85,M1. 
  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 0521358833. 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. 
  7. ↑ James Gordon MacGregor (1887). An Elementary Treatise on Kinematics and Dynamics. Macmillan. p. v. http://books.google.com/books?id=3yMQAAAAYAAJ&printsec=frontcover&dq=kinematics+dynamics&lr=&as_brr=0#PPR5,M1. 
  8. ↑ Stephen Timoshenko, Donovan Harold Young (1956). Engineering mechanics. McGraw Hill. http://books.google.ca/books?id=I548AAAAIAAJ&q=engineering+mechanics+inauthor:Timoshenko&dq=engineering+mechanics+inauthor:Timoshenko&lr=&as_brr=0&ei=hX_SSO2_E432sgPuzrGTBw&pgis=1. 
  9. ↑ Lakshmana C. Rao, J. Lakshminarasimhan, Raju Sethuraman, Srinivasan M. Sivakumar (2004). Engineering mechanics. PHI Learning Pvt. Ltd.. p. vi. ISBN 8120321898. http://books.google.com/books?id=F7gaa1ShPKIC&printsec=frontcover&dq=statics+dynamics&lr=&as_brr=0&sig=ACfU3U2haQ0TLc90YwYiTtuhvIgfA6ZXEQ#PPR6,M1. 
  10. ↑ David Hestenes (1999). New Foundations for Classical Mechanics. Springer. p. 198. ISBN 0792355148. http://books.google.com/books?id=eU2qm8wavRwC&pg=PA198&dq=dynamics+kinematics&lr=&as_brr=0&sig=ACfU3U2C3aW_zumPCy2Doe4K4NKsjJXKeQ. 
  11. ↑ R. Douglas Gregory (2006). Classical Mechanics: An Undergraduate Text. Cambridge University Press. ISBN 0521826780, 9780521826785. http://books.google.com/books?id=uAfUQmQbzOkC&q=dynamics#search. 
  12. ↑ Landau, L. D.; Lifshitz, E. M.; Sykes, J.B.; Bell, J. S. (1976), Mechanics, 1, Butterworth-Heinemann, ISBN 0750628960, 9780750628969, http://books.google.com/books?id=LmAV8q_OOOgC 
  13. ↑ Jorge Valenzuela José, Eugene Jerome Saletan (1998). Classical Dynamics: A Contemporary Approach. Cambridge University Press. ISBN 0521636361, 9780521636360. http://books.google.com/books?id=ZW0L5Xe9zhwC. 
  14. ↑ T. W. B. Kibble, Frank H. Berkshire (2004). Classical Mechanics. Imperial College Press. ISBN 1860944353, 9781860944352. http://books.google.com/books?id=0a8dk0eDxgEC. 
  15. ↑ Walter Greiner, S. Allan Bromley (2003). Classical Mechanics: Point Particles and Relativity. Springer. ISBN 0387955860, 9780387955865. http://books.google.com/books?id=L_APSPGoI5sC. 
  16. ↑ Gerald Jay Sussman, Jack Wisdom Meinhard, Edwin Mayer (2001). Structure and Interpretation of Classical Mechanics. MIT Press. ISBN 0262194554, 9780262194556. http://books.google.com/books?client=firefox-a&id=H_6Ux04cPv8C&q=dynamics#search. 
  17. ↑ Harald Iro (2002). A Modern Approach to Classical Mechanics. World Scientific. ISBN 9812382135, 9789812382139. http://books.google.com/books?id=-L5ckgdxA5YC. 
  18. ↑ Feynman, RP; Leighton, RB; Sands, M (2003), The Feynman Lectures on Physics, Vol. 1 (Reprint of 1963 lectures ed.), Perseus Books Group, p. Ch. 9 Newton's Laws of Dynamics, ISBN 0738209309