Parabolic trajectories and Lie’s contact transformations


== Abstract ==

The great mathematician Sophus Lie invented infinitesimal transformations to solve differential equations that, we know, are the mean, at least from the time of Newton, to study in deph the diverse aspects of the natural world.
The idea of Lie was to apply to these equations the theory of groups that Galois has apllied to algebraic equations.
Though Hamilton, in some way, was close to the idea, contact transformations were brought out explicitly by Sophus Lie as early as in 1872 when in a seminal work he pointed out the importance of transformations beginning and epoch change that goes on to the present [10].

== Full document ==
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