From Wikipedia, the free encyclopedia
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.
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
- ^ 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.
- ^ 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.
- ^ ^{a}
^{b}
^{c}
John Robert Taylor (2005). Classical
Mechanics. University Science Books. ISBN 189138922X,
9781891389221. http://books.google.com/books?id=P1kCtNr-pJsC&q=dynamics#search.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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
- ^ 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.
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Classical
Mechanics. Imperial College Press. ISBN 1860944353,
9781860944352. http://books.google.com/books?id=0a8dk0eDxgEC.
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Particles and Relativity. Springer. ISBN 0387955860,
9780387955865. http://books.google.com/books?id=L_APSPGoI5sC.
- ^ Gerald Jay Sussman, Jack Wisdom Meinhard,
Edwin Mayer (2001). Structure and
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9780262194556. http://books.google.com/books?client=firefox-a&id=H_6Ux04cPv8C&q=dynamics#search.
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0738209309