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The goal of this tutorial is to present the Lagrangian and Hamiltonian
formalism of mechanics. After reading this tutorial the reader will be able
to write down equations of motion for various conservative mechanical systems.
In particular, the reader will learn how to write the equations of
motion in a rotating coordinate system
(section 5) and will learn the canonical
(Hamiltonian) form of the equations of motion in the restricted
circular three-body problem (section 6).
The material in this tutorial is standard and it can be found in most
books on mechanics. However, it is hard to find all the necessary
facts in one book and a variety of notations are being used.
This justifies the existence of this document.