Abstract:
Some remarks on the application of the Hori method in the theory of nonlinear oscillations are presented. Two simplified algorithms for determining the generating function and the new system of differential equations are derived from a general algorithm proposed by Sessin. The vector functions which define the generating function and the new system of differential equations are not uniquely determined, since the algorithms involve arbitrary functions of the constants of integration of the general solution of the new undisturbed system. Different choices of these arbitrary functions can be made in order to simplify the new system of differential equations and define appropriate near-identity transformations. These simplified algorithms are applied in determining second-order asymptotic solutions of two well-known equations in the theory of nonlinear oscillations: van der Pol equation and Duffing equation.

Abstract:
Numerical and first-order analytical results are presented for optimal low-thrust limited-power trajectories in a gravity field that includes the second zonal harmonic 2 in the gravitational potential. Only transfers between orbits with small eccentricities are considered. The optimization problem is formulated as a Mayer problem of optimal control with Cartesian elements—position and velocity vectors—as state variables. After applying the Pontryagin Maximum Principle, successive canonical transformations are performed and a suitable set of orbital elements is introduced. Hori method—a perturbation technique based on Lie series—is applied in solving the canonical system of differential equations that governs the optimal trajectories. First-order analytical solutions are presented for transfers between close orbits, and a numerical solution is obtained for transfers between arbitrary orbits by solving the two-point boundary value problem described by averaged maximum Hamiltonian, expressed in nonsingular elements, through a shooting method. A comparison between analytical and numerical results is presented for some maneuvers.

Abstract:
some properties of generalized canonical systems - special dynamical systems described by a hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. a complete closed-form solution for lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. for circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Abstract:
Some properties of generalized canonical systems - special dynamical systems described by a Hamiltonian function linear in the adjoint variables - are applied in determining the solution of the two-dimensional coast-arc problem in an inverse-square gravity field. A complete closed-form solution for Lagrangian multipliers - adjoint variables - is obtained by means of such properties for elliptic, circular, parabolic and hyperbolic motions. Classic orbital elements are taken as constants of integration of this solution in the case of elliptic, parabolic and hyperbolic motions. For circular motion, a set of nonsingular orbital elements is introduced as constants of integration in order to eliminate the singularity of the solution.

Abstract:
sediment samples from the barigui river in curitiba, south of brazil, were evaluated following granulometric composition, organic carbon content, nitrogen, phosphorus and metals such as zinc, lead, chrome, nickel and cadmium. the sediments shown high percentage of phosphorus and nitrogen. also the elemental organic c:n:p exceed the redfield ratios possible because the large amount of sewage input into river. the presence of metals is also high, however the metal cadmium has not been found. but the other metals are in greater concentrations and possibly the presence of these metals is given by industrial and domestic sewage.

Abstract:
the objective of this work was to evaluate the environmental distribution of benzo(a)pirene, a polycyclic aromatic hydrocarbon, by the eqc model. the modeling of the contaminant distribution was accomplished by means of the fugacity model applied to a hypothetical scenario constituted by air, water, soil and sediment. the modeling and simulations revealed that the soil is the preferential compartment. we also discuss the implications of the results about fate and ecological risks associated with benzo(a)pirene. we concluded that the emissions of hpas can not be ignored and bioaccumulation among others risks can be induced.

Abstract:
A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

Abstract:
A complete first-order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through canonical transformation theory. The optimization problem is formulated as a Mayer problem of optimal control theory with Cartesian elements—position and velocity vectors—as state variables. After applying the Pontryagin maximum principle and determining the maximum Hamiltonian, classical orbital elements are introduced through a Mathieu transformation. The short periodic terms are then eliminated from the maximum Hamiltonian through an infinitesimal canonical transformation built through Hori method. Closed-form analytical solutions are obtained for the average canonical system by solving the Hamilton-Jacobi equation through separation of variables technique. For transfers between close orbits a simplified solution is straightforwardly derived by linearizing the new Hamiltonian and the generating function obtained through Hori method.

Abstract:
A study of optimal two-impulse trajectories with moderate flight time for Earth-Moon missions is presented. The optimization criterion is the total characteristic velocity. Three dynamical models are used to describe the motion of the space vehicle: the well-known patched-conic approximation and two versions of the planar circular restricted three-body problem (PCR3BP). In the patched-conic approximation model, the parameters to be optimized are two: initial phase angle of space vehicle and the first velocity impulse. In the PCR3BP models, the parameters to be optimized are four: initial phase angle of space vehicle, flight time, and the first and the second velocity impulses. In all cases, the optimization problem has one degree of freedom and can be solved by means of an algorithm based on gradient method in conjunction with Newton-Raphson method.

Abstract:
the purposes of this study were: (i) explore the relationship between body mass index (bmi) and perceived physical competence (ppc), and/or effective basketball competence (ecb); (ii) understand the relationship between ppc and ecb; and, (iii) establish the sources of information that the young use to define the ppc. a sample of 156 physical education students, with ages ranging from 12 to 18 years (m=14.36; sd=1.76), completed the perception of physical competence subscale (ppcs) and the physical competence source？s subscale (pcss). they also realized a protocol to measure effective competence in basketball. the main results revealed: (i) significant differences between boys and girls, while comparing bmi, with higher mean scores for boys; (ii) higher mean scores of ppc and bec for boys; (iii) significant differences for the following constructs of the pcss: pre-competition anxiety and sport attraction; and, (iv) significant differences between different groups of ages, for parent？s evaluation factor.