id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-189434-nrkvbdu4	Steinmann, Paul	Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling	2020-06-06		.txt	text/plain	5589	351	48	In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as Hamilton's principle in terms of a suited Lagrangian are considered in minimal and extended phase and state space coordinates, respectively. Taken together, the time re-parameterized SIR model obeys Hamiltonian structure and identifies the relation between the gradient G(Z) ∈ R 2 of the Hamiltonian H(Z) in minimal phase space coordinates and the forcing term F (Z) ∈ R 2 as Clearly, the Euler-Lagrange equation in minimal state space coordinates coincides with the single, non-linear ODE formulation of the time re-parameterized SIR model in Eq. 7. Using again Hamilton's equation Q • = 2Λ · J and exploiting the skew-symmetry of the symplectic matrix, i.e. Λ · J = −J · Λ, recovers once more the already previously established relation between the gradient G(Q) ∈ R 2 of the Hamiltonian H(Q) (in extended state space coordinates) and the forcing term	./cache/cord-189434-nrkvbdu4.txt	./txt/cord-189434-nrkvbdu4.txt