Singular fuel-optimal space trajectories based on linearization about a point in circular orbit

The problem of transferring a space vehicle between two points in a given gravitational field such that the minimum amount of fuel is used has been called the fundamental navigational problem of astronautics. In such a problem it may be required to find the optimum thrust magnitude and thrust direction which yields a minimum fuel trajectory. Furthermore, certain end conditions may be specified which the optimal trajectory must satisfy. In a large number of published papers the velocity of the vehicle is supposed known both at the beginning of the transfer and at the end whereas the time taken to complete the manoeuvre may or may not be given. Also, other performance criteria have been chosen besides minimum fuel. For example, minimum time of transit or maximum orbital altitude at perigee. Papers mentioned in this review deal mainly with flight in two dimensions apart from those sections on general theory. Furthermore, all space vehicles considered are assumed to have a fixed exhaust velocity unless otherwise stated.

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Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Journal of Optimization Theory and Applications ◽

10.1007/s10957-021-01867-2 ◽

2021 ◽

Author(s):

Mauro Pontani

Keyword(s):

Optimization Problem ◽

Space Mission ◽

Low Thrust ◽

Optimal Space Trajectories ◽

Sequential Solution ◽

Necessary Conditions For Optimality ◽

Single Arc ◽

Finite Thrust ◽

Solution Methodology ◽

Optimal Space

AbstractThe detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

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Evolution of Rotational Motion of a Planet in a Circular Orbit Under the Influence of Internal Elastic and Dissipative Forces

Mechanics of Solids ◽

10.3103/s0025654420020053 ◽

2020 ◽

Vol 55 (2) ◽

pp. 234-247

Author(s):

N. I. Amel’kin

Keyword(s):

Rotational Motion ◽

Circular Orbit ◽

Dissipative Forces

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The curiously circular orbit of Kepler-16b

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stt1456 ◽

2013 ◽

Vol 435 (3) ◽

pp. 2328-2334 ◽

Cited By ~ 17

Author(s):

A. C. Dunhill ◽

R. D. Alexander

Keyword(s):

Circular Orbit

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Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

Applied Sciences ◽

10.3390/app11094237 ◽

2021 ◽

Vol 11 (9) ◽

pp. 4237

Author(s):

Mingjie Zhang ◽

Jiangang Yang ◽

Wanfu Zhang ◽

Qianlei Gu

Keyword(s):

Circular Orbit ◽

Present Method ◽

Decomposition Method ◽

Parameter Analysis ◽

Elliptical Orbit ◽

Computational Time ◽

Solution Technique ◽

Rotordynamic Coefficients ◽

Cfd Method ◽

Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

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