Special Mechanical Systems
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In this chapter we adhere systematically to the convention of denoting and writing the Lagrangian functions that we shall meet as L (ẋ, x, t) or L (ẋ, x) or L (̇q, q, t), rather than as functions of generic variables α, β, t: the notation is obviously improper since in such cases the variables ẋ and x are not Cartesian coordinates but local (or toral) coordinates, and often the mechanical systems will be described directly in local coordinates omitting the obvious but tedious discussion necessary when the local coordinates are not global (i.e., they are not globally equivalent to Cartesian coordinates).
KeywordsDirichlet Problem Lagrangian Function Canonical Transformation Geodesic Motion Integrability Criterion
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