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In page Hamiltonian system:

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The trajectory r ( t ) {\displaystyle {\boldsymbol {r}}(t)} is the solution of the initial value problem defined by the Hamilton's equations and the initial condition r ( 0 ) = r 0 R 2 N {\displaystyle {\boldsymbol {r}}(0)={\boldsymbol {r}}_{0}\in \mathbb {R} ^{2N}} .