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                CLASSICAL DYNAMICS
                         Introduction
                  Chennai Mathematical Institute
                         January - April 2005
          Chennai, April 12, 2006
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                 Preface
                 This set of lecture notes is an attempt to convey the excitement of classical dynamics
                 from a contemporary point of view. The contents of this course were developed for
                 undergraduate students in their second semester at Chennai Mathematical Institute.
                      With recent interest and developments in non-linear dynamics and chaos it was
                 thought appropriate to develop a mathematical framework for describing dynamical
                 systems in general, linear or non-linear. Beginning with the description of differential
                 equations governing the time evolution of a dynamical system, these notes discuss
                 how the qualitative features of a dynamical system may be gleaned by simply study-
                 ing its local behaviour and stability around the fixed points. The time evolution of
                 any dynamical system is described by the flow of th system in phase space. Systems
                 described by Hamiltonians are but a special case of more general dynamical systems.
                 For completeness Lagrangian mechanics is also discussed and connections with Hamil-
                 tonian formalism established. In the end we discuss semi-quantitatively some simple
                 systems which show chaotic behaviour.
                      The contents of this lecture notes evolved from an earlier set of lectures given by
                 Professor Matthias Brack to students at the University of Regensburg in Germany.
                 The students of B.Sc.(Physics), A.B. Belliappa, Argya Mondal and Shouvik Sur have
                 contributed enormously to enrich the contents of these notes. Apart from going
                 through the material they have written and edited parts of the material.
                      The lecture notes is our tribute to the memory of late Deep Roy, a student of the
                 same batch, who passed away in July 2005. Deep was very enthusiastic about docu-
                 menting the course of lectures and had volunteered many corrections and comments
                 on the preliminary version. We would like to think that he would have appreciated
                 what we have together done.
                      I would like to thank all the students of B.Sc (Physics), batch of 2004, for par-
                 ticipating in this project.  Encouragement from Deep Roy’s father Amitava Roy,
                 Madhavan Mukund and P.P. Divakaran to undertake this project is gratefully ac-
                 knowledged.
                 M.V.N. Murthy
                 The Institute of Mathematical Sciences
                 Chennai
                 April 2006.
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