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Geodesics as Hamiltonian flows
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the <a href="/facts/Geodesic_equation/fbWR6l80">geodesic equations</a> are second-order non-linear <a href="/facts/Differential_equation/9MGbE3Ca">differential equations</a>, and are commonly presented in the form of <a href="/facts/Euler%25E2%2580%2593Lagrange/Ymq3r3Dh">Euler–Lagrange</a> equations of motion. However, they can also be presented as a set of coupled first-order equations, in the form of <a href="/facts/Hamilton%2527s_equations/2ReerlNA">Hamilton's equations</a>. This latter formulation is developed in this article. </p>