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Our approach so far has emphasized the Hamiltonian point of view. However, there is an independent point of view, that of Lagrangian mechanics, based on variational principles. This alternative viewpoint, computational convenience, and the fact that the Lagrangian is very useful in covariant relativistic theories can be used as arguments for the importance of the Lagrangian formulation. Ironically, it was Hamilton  who discovered the variational basis of Lagrangian mechanics.
KeywordsVector Field Integral Curve Jacobi Equation Finite Dimension Hamiltonian Vector Field
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