Internet congestion control model
WSEAS Transactions on Information Science and Applications
Multitime Hamilton-Jacobi theory
ISTASC'09 Proceedings of the 9th WSEAS International Conference on Systems Theory and Scientific Computation
Two-time stochastic Lagrangian dynamics
ISTASC'09 Proceedings of the 9th WSEAS International Conference on Systems Theory and Scientific Computation
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The second order differential equations of Euler-Lagrange type are sometimes equivalent to Hamilton differential equations (of first order) in double dimension. The equivalence is realized via Legendrian duality. We present our point of view upon adjointness, Hamiltonian systems and Riemannian and Legendrian duality in the single-time case. Sections 1 and 2 review well-known facts regarding adjointness and Hamiltonian systems. The main result is given in Section 3. There we exhibit the family of Lagrangians that are generated by the control Hamiltonian, and the family of Lagrangians generated by the geometric dynamics Hamiltonian. Section 4 gives two Ibragimov Lagrangians. Section 5 formulates conclusions.