Analytical Dynamics
Analytical Dynamics
Analytical Dynamics
For dynamics as the time evolution of physical processes, dealing with determination of the motion of bodies resee Dynamics (mechanics).
sulting from the action of specied forces;[7] another approach separated statics, and combined kinetics and kine[8][9]
This approach is
In classical mechanics, analytical dynamics, or more matics under the rubric dynamics.
common in engineering books on mechanics, and is still
briey dynamics, is concerned about the relationship between motion of bodies and its causes, namely the forces in widespread use among mechanicians.
acting on the bodies and the properties of the bodies (particularly mass and moment of inertia). The foundation
2.1 Fundamental importance in engineerof modern-day dynamics is Newtonian mechanics and its
ing, diminishing emphasis in physics
reformulation as Lagrangian mechanics and Hamiltonian
[1][2]
mechanics.
Today, dynamics and kinematics continue to be considered the two pillars of classical mechanics. Dynamics is
still included in mechanical, aerospace, and other engi1 History
neering curricula because of its importance in machine
design, the design of land, sea, air and space vehicles and
The eld has a long and important history, as remarked other applications. However, few modern physicists conby Hamilton: The theoretical development of the laws of cern themselves with an independent treatment of dymotion of bodies is a problem of such interest and impor- namics or kinematics, nevermind statics or kinettance that it has engaged the attention of all the eminent ics. Instead, the entire undierentiated subject is remathematicians since the invention of the dynamics as a ferred to as classical mechanics. In fact, many undergradmathematical science by Galileo, and especially since the uate and graduate text books since mid-20th century on
wonderful extension which was given to that science by classical mechanics lack chapters titled dynamics or
Newton. William Rowan Hamilton, 1834 (Transcribed kinematics.[3][10][11][12][13][14][15][16][17] In these books,
in Classical Mechanics by J.R. Taylor, p. 237[3] )
although the word dynamics is used when acceleration
[3]
Some authors (for example, Taylor (2005) and Green- is ascribed to a force, the word kinetics is never menexwood (1997)[4] ) include special relativity within classical tioned. However, clear exceptions exist. Prominent
[18]
amples
include
The
Feynman
Lectures
on
Physics.
dynamics.
List of Fundamental Dynamics Principles
Acceleration
Momentum
Reaction
"kinematics" (dealing with the implications of observed motions without regard for circumstances
causing them).[6]
5
Canonical transformations
Hamilton-Jacobi Theory
4.1
Related subjects
Statics
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. 56. ISBN 0-486-65067-7.
[3] 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 81-2032189-8.
REFERENCES
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