Geodesics As Hamiltonian Flows
In mathematics, the geodesic equations are second-order non-linear differential equations, and are commonly presented in the form of Euler–Lagrange equations of motion. However, they can also be presented as a set of coupled first-order equations, in the form of Hamilton's equations. This latter formulation is developed in this article.
Read more about Geodesics As Hamiltonian Flows: Overview, Geodesics As An Application of The Principle of Least Action, Hamiltonian Approach To The Geodesic Equations
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“It is a mischievous notion that we are come late into nature; that the world was finished a long time ago. As the world was plastic and fluid in the hands of God, so it is ever to so much of his attributes as we bring to it. To ignorance and sin, it is flint. They adapt to themselves to it as they may; but in proportion as a man has anything in him divine, the firmament flows before him and takes his signet and form.”
—Ralph Waldo Emerson (1803–1882)