Mathematical methods in the mechanics of infinite-dimensional nonpotential systems.

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Variational principles of physics (49S05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of particles and systems (70-01) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items (23)

On connection between variationality of a six-order ordinary differential equation and Hamilton-Ostrogradskii equations ⋮ On infinite-dimensional Lagrangian systems with nonpotential forces ⋮ Invariance of functionals and related Euler-Lagrange equations ⋮ Nonclassical Hamilton’s Actions and the Numerical Performance of Variational Methods for Some Dissipative Problems ⋮ On the existence of a variational principle for an operator equation with second derivative with respect to ``time ⋮ Construction of variational multipliers for the operator of one system of nonlinear evolutionary partial differential equations ⋮ Bi-variationality, symmetries and approximate solutions ⋮ On quasipotential operators and Hamiltonian-admissible equations in the mechanics of infinite-dimensional systems ⋮ ON THE CONNECTION BETWEEN FIRST INTEGRALS, INTEGRAL INVARIANTS AND POTENTIALITY OF EVOLUTIONARY EQUATIONS ⋮ On a representation of an operator equation with first time derivative in the form of a \(B_u\)-Hamiltonian equation ⋮ Variational symmetries of Euler and non-Euler functionals ⋮ On \(B_u\)-Hamiltonian equations in mechanics of infinite-dimensional systems ⋮ Nonpotentiality of Sobolev system and construction of semibounded functional ⋮ ON THE POTENTIALITY OF A CLASS OF OPERATORS RELATIVE TO LOCAL BILINEAR FORMS ⋮ An operator equation with the second time derivative and Hamiltonian-admissible equations ⋮ On connection between symmetries of functionals and equations ⋮ Necessary and sufficient conditions for the existence of a symmetry group for a system of partial differential-difference equations ⋮ Variational principles for nonpotential operators ⋮ Hamilton equations for infinite-dimensional systems, and their variational equations ⋮ Symmetries and first integrals in the mechanics of infinite-dimensional systems ⋮ On connection between variational symmetries and algebraic structures ⋮ Helmholtz potentiality conditions for systems of difference-differential equations ⋮ Lie-admissible algebras associated with dynamical systems

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