id	author	title	date	pages	extension	mime	words	sentence	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	5590	171	31	The supremum condition identifies I • with the derivative ∂ S H(Z) of the Hamiltonian in minimal phase space coordinates from Eq. 9 with respect to the generalized momentum, and renders Re-solving the above supremum condition for S in terms of I • delivers Based on the Lagrangian in minimal state space coordinates, Hamilton's principle results in the stationarity condition 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. Alternatively, extended state space coordinates collectively assembled in the column matrix Q ∈ R 2 , i.e. the generalized coordinates jointly defined as the stock of individuals in the Infected and Susceptible compartments, span the two-dimensional state space Ë, J t = J · Q and J 2 = −I, an additional constraint for the extended phase space coordinates emerges The Hamiltonian H(Q, P ) in extended phase space coordinates thus follows from Legendre transformation by incorporating the constraint via the Lagrange multiplier Λ, i.e. Taking into account the explicit form of the Lagrangian L(Q, Q • ) in extended state space coordinates from Eq. 25 then renders the explicit representation of the Hamiltonian H(Q, P ) in extended phase space coordinates Invoking ∂ Q C(Q, P )	cache/cord-189434-nrkvbdu4.txt	txt/cord-189434-nrkvbdu4.txt
