16 research outputs found

    Symmetries in Classical Field Theory

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    The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

    Dependent coordinates in path integral measure factorization

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    The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group. The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory. The integral relation between the kernels of the original and reduced semigroup are obtained.Comment: LaTeX2e, 28 page

    Stochastic Differentiation - A Generalized Approach

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    The space (D*) of Wiener distributions allows a natural Pettis-type stochastic calculus. For a certain class of generalized multiparameter processes X: R N →(D*) we prove several differentiation rules (Itô formulas); these processes can be anticipating. We then apply these rules to some examples of square integrable Wiener functionals and look at the integral versions of the resulting formulas

    Stochastic Differentiation — A Generalized Approach

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    Better Than Optimal By Taking A Limit?

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    Periodic orbits above the ecliptic plane in the solar sail restricted 3-body problem

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    We consider periodic orbits in the circular restricted three-body problem, where the third (small) body is a solar sail. In particular, we consider orbits about equilibrium points in the Earth-sun rotating frame, which are high above the ecliptic plane, in contrast to the classical "halo" orbits about the collinear equilibria. It is found that due to coupling in the equations of motion, periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. It is found that there is much freedom in specifying the position and period/amplitude of the orbit of the sail, high above the ecliptic and looking down on the Earth.Aparticular use of such solutions is presented, namely, the year-round constant imaging of, and communication with, the poles. We find that these orbits present a significant improvement on the position of the sail when viewed from the Earth, compared to a sail placed at equilibrium
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