Solitons pp 2-6 | Cite as

Inaugural Address — The Dynamics of Dynamics

  • E. C. G. Sudarshan
Conference paper
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Abstract

A dynamical system is defined by a collection of configurational coordinates and equations of motion obeyed by them. These equations of motion may be generated by a suitable principle or may themselves be postulated. Given such equations of motion we would like to solve them so that the dynamical variables at any time may be determined as a function of the initial variables and time. For a system which is a generalization of a Newtonian system these would be even in number. The central problem of dynamics is the determination and characterization of the solutions. Naturally if we can solve the problem completely then we could consider various aspects of the solutions including the dependence of the solution on the initial data. Except for the really trivial cases, even in relatively elementary examples there are interesting dependences and qualitatively new features emerging. For example if we consider the elementary problem of uniform acceleration, say a projectile moving vertically in terms of the initial position s, initial velocity u and the acceleration due to gravity -g, the distance s travelled in time t is:
$$ s = {s_0} + ut - \tfrac{1}{2}g{t^2} $$
(1)

Keywords

Manifold Soliton 

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References

  1. [1]
    M. Lakshmanan and R. Sahadevan, Painlevé analysis, Lie-symmetries, and integrability of coupled nonlinear oscillators of polynomial type, Physics Reports, to be published; R. Sahadevan, Painlevé analysis and integrability of certain coupled nonlinear oscillators, Ph.D. Thesis, University of Madras, 1986 (Unpublished).Google Scholar
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    M. Lakshmanan and R. Sahadevan, Phys. Rev. A31 (1985) 861MathSciNetADSGoogle Scholar
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    R. Sahadevan and M. Lakshmanan, Phys. Rev. A33 (1986) 3563.ADSGoogle Scholar
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    J. Williamson, Amer. J. Math. 58 (1936) 141.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • E. C. G. Sudarshan
    • 1
  1. 1.The Institute of Mathematical SciencesMadrasIndia

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