Search results for "Kepler's equation"

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Remarks on quadratic Hamiltonians in spaceflight mechanics

2006

A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.

Physics[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Integrable systemApproximations of π010102 general mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]MechanicsKepler's equationSpaceflight01 natural scienceslaw.invention010101 applied mathematicsNonlinear systemsymbols.namesakeQuadratic equationClassical mechanicslawsymbols[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsHamiltonian (quantum mechanics)ComputingMilieux_MISCELLANEOUS
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Geodesic flow of the averaged controlled Kepler equation

2008

A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyGeodesicGeneral MathematicsCut locusConformal map02 engineering and technologyKepler's equationFundamental theorem of Riemannian geometry01 natural sciencesConvexityIntrinsic metricsymbols.namesake020901 industrial engineering & automationSingularity0101 mathematicsorbit transferMathematicsApplied Mathematics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]cut and conjugate lociRiemannian metrics49K15 70Q05symbols[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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