Deformation of a line-element in the phase space at the triangular libration point

1981 ◽  
Vol 23 (2) ◽  
pp. 131-137 ◽  
Author(s):  
V. Szebehely ◽  
R. McKenzie
Keyword(s):  
Phase Space ◽  
Line Element ◽  
Libration Point ◽  
Triangular Libration Point

Phase space sensitivities of the Sun-Jupiter triangular libration point

1997 ◽  
Vol 88 (2-3) ◽  
pp. 255-265 ◽  
Author(s):  
Dan G. Tuckness
Keyword(s):  
Phase Space ◽  
Libration Point ◽  
The Sun ◽  
Triangular Libration Point

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

Low-thrust transfer to the Earth-Moon triangular libration point via horseshoe orbit

2020 ◽  
Vol 177 ◽  
pp. 111-121
Author(s):  
Xingji He ◽  
Yuying Liang ◽  
Ming Xu ◽  
Yaru Zheng
Keyword(s):  
Libration Point ◽  
Low Thrust ◽  
Triangular Libration Point ◽  
The Earth ◽  
Horseshoe Orbit

Periodic motion around the triangular libration point in the restricted problem of four bodies

1967 ◽  
Vol 72 ◽  
pp. 180 ◽  
Author(s):  
Ronald Kolenkiewicz ◽  
Lloyd Carpenter
Keyword(s):  
Periodic Motion ◽  
Restricted Problem ◽  
Libration Point ◽  
Triangular Libration Point

Riemannian metric in Gibbsian phase-space

1970 ◽  
Vol 319 (1538) ◽  
pp. 307-317 ◽  
Keyword(s):  
Phase Space ◽  
Line Element ◽  
Riemannian Metric ◽  
Point Transformations ◽  
Classical Trajectories ◽  
Classical Phase Space ◽  
Extended Point

In the classical phase-space of Gibbs, a Riemannian line-element is defined, invariant under extended point transformations and preserving the Gbbsian volume. To make the line-element dimensionally homogeneous, Planck ’s constant h is incorporated in it. For a system consisting of particles, geodesics are investigated; they coincide with classical trajectories in the limit when h tends to zero, and have some interesting simple properties when h is finite.

scholarly journals A transfer network linking Earth, Moon, and the triangular libration point regions in the Earth-Moon system

2018 ◽  
Vol 62 (7) ◽  
pp. 1826-1852 ◽  
Author(s):  
Lucia R. Capdevila ◽  
Kathleen C. Howell
Keyword(s):  
Libration Point ◽  
Moon System ◽  
Triangular Libration Point ◽  
The Earth

scholarly journals Formation-Keeping Strategies At The Earth-Moon L4 Triangular Libration Point

2021 ◽  
Author(s):  
Frank Y. W. Wong
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Libration Point ◽  
Control Technique ◽  
Solar Sails ◽  
Hybrid Propulsion ◽  
Triangular Libration Point ◽  
Spacecraft Formation ◽  
The Earth ◽  
Formation Keeping

This thesis examines the use of thrusters and solar sails for spacecraft formation keeping control at the Earth-Moon L4 point. Particular emphasis was placed on the study of underactuated control, in which fewer control inputs than the system's degrees of freedom are available. A linear LQR control scheme, an integral augmented sliding mode controller and a bang-bang controller were applied to the dynamic spacecraft system. The nonlinear controllers produced errors falling with tighter tolerances than the linear controllers in the perturbed environment. Performing similarly well as the underactuated thrusters system was the solar-sails-controlled spacecraft formation using a bang-bang controller. This shows that solar sails could be a viable propellantless technique for relative control. A linear control technique was able to bound errors to within a couple of hundred metres, using a hybrid propulsion system. Of the cases studied, only the fully-actuated thrusters-based system was able to explicitly track a circular trajectory, but had [Delta]V requirement of more than 100 times greater than that needed for tracking the natural, elliptical trajectory.

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