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    Wyświetlanie 1-6 z 6
    Tytuł:
    Systems of rays in the presence of distribution of hyperplanes
    Autorzy:
    Janeczko, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1359671.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    optical rays
    Hamiltonian systems
    distributions
    singularities of Lagrange projections
    Opis:
    Horizontal systems of rays arise in the study of integral curves of Hamiltonian systems $v_H$ on T*X, which are tangent to a given distribution V of hyperplanes on X. We investigate the local properties of systems of rays for general pairs (H,V) as well as for Hamiltonians H such that the corresponding Hamiltonian vector fields $v_H$ are horizontal with respect to V. As an example we explicitly calculate the space of horizontal geodesics and the corresponding systems of rays for the canonical distribution on the Heisenberg group. Local stability of systems of horizontal rays based on the standard singularity theory of Lagrangian submanifolds is also considered.
    Źródło:
    Banach Center Publications; 1995, 32, 1; 245-260
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
    Autorzy:
    Barile, Sara
    Salvadore, Addolorata
    Powiązania:
    https://bibliotekanauki.pl/articles/255922.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    second order Hamiltonian systems homoclinic solutions
    variational methods
    compact embeddings
    Opis:
    We look for homoclinic solutions [formula] to the class of second order Hamiltonian systems [formula] where [formula] and a, b : R → R are positive bounded functions, [formula] are positive homogeneous functions and [formula]. Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if = 0 and the existence of at least three solutions if ƒ is not trivial but small enough.
    Źródło:
    Opuscula Mathematica; 2020, 40, 1; 21-36
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
    Autorzy:
    Bogoliubov, N. N. (Jr.)
    Blackmore, D. L.
    Somoylenko, V. Hr.
    Prykarpatsky, A. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/255472.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    kinetic Boltzmann-Vlasov equations
    hydrodynamic model
    Hamiltonian systems
    invariants
    dynamical equivalence
    Opis:
    A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
    Źródło:
    Opuscula Mathematica; 2007, 27, 2; 187-195
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Periodic solutions for second-order Hamiltonian systems with a p-Laplacian
    Autorzy:
    Zhang, Xingyong
    Tang, Xianhua
    Powiązania:
    https://bibliotekanauki.pl/articles/747033.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Second-order Hamiltonian systems
    p-Laplacian
    periodic solution
    Sobolev’s inequality
    Wirtinger’s inequality
    the least action principle
    Opis:
    In this paper, by using the least action principle, Sobolev’s inequality and Wirtinger’s inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2010, 54, 1
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems
    Autorzy:
    Freihold, M.
    Hofer, E. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/930126.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    system Hamiltona
    algorytm rozgałęzienia
    system dynamiczny
    VALENCIA-IVP
    consistency tests for the reduction of overestimation
    identification of dynamical constraints
    Hamiltonian systems
    branch algorithm
    prune algorithm
    Opis:
    Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically eaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 485-499
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical error bound of optimal control for homogeneous linear systems
    Autorzy:
    Daraghmeh, Adnan
    Qatanani, Naji
    Powiązania:
    https://bibliotekanauki.pl/articles/229410.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-invariant systems
    quadratic cost function
    linear quadratic regulator
    algebraic Riccati equation
    Hamiltonian function
    L2 norm
    Opis:
    In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called "the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.
    Źródło:
    Archives of Control Sciences; 2019, 29, 2; 323-337
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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