scholarly journals A New 3D Shaping Method for Low-Thrust Trajectories between Non-Intersect Orbits

Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 315
Author(s):  
Tongxin Zhang ◽  
Di Wu ◽  
Fanghua Jiang ◽  
Hong Zhou
Keyword(s):  
Trajectory Optimization ◽  
Three Dimensional ◽  
Normalization Method ◽  
Spherical Coordinates ◽  
Initial Estimate ◽  
Low Thrust ◽  
Numerical Examples ◽  
The Third ◽  
Orbit Fitting ◽  
Maximum Thrust

This paper proposes a new shape-based method in spherical coordinates to solve three-dimensional rendezvous problems. Compared with the existing shape-based methods, the proposed method does not need parameter optimization. Moreover, it improves the flexibility of orbit fitting, greatly reduces the velocity increment and maximum thrust acceleration, and ensures the orbit safety to a certain extent. The shaping function can provide the initial estimate for numerical trajectory optimization and improve the convergence rate in a certain range when combined with the normalization method. The superiority of the proposed method over the existing methods is demonstrated by two numerical examples. Its effectiveness at initial estimation generation in the indirect optimization of a low-thrust trajectory is demonstrated by the third example.

The Third Two-Dimensional Problem of Three-Dimensional Blade Systems of Hydraulic Machines—Part 2: Analytical Results

1981 ◽  
Vol 103 (1) ◽  
pp. 42-51
Author(s):  
P. K. Agarwal ◽  
G. V. Viktorov
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Blade Profile ◽  
Flow Conditions ◽  
Numerical Examples ◽  
The Third ◽  
Hydraulic Machines ◽  
Method Of Solution ◽  
Axisymmetric Stream

This is the second part of a study of the “third” two-dimensional problem of three-dimensional blade systems of hydraulic machines. Part I described the formulation of the problem and the proposed method of solution to determine the velocity field on surfaces orthogonal to mean axisymmetric stream surfaces. Part II presents the numerical method of solving the integral equations; a few numerical examples for actual impellers/runners are also given. The results are presented in a series of figures and tables showing the distribution of the velocity component c2 along the blade profile on the surface q1 = const. The purpose of these numerical examples is to demonstrate the method and to help create a general understanding and awareness of the flow conditions existing in the runner passage.

Algebraic Geodesics on Three-Dimensional Quadrics

2015 ◽  
Vol 70 (12) ◽  
pp. 1049-1054
Author(s):  
Yue Kai
Keyword(s):  
Implicit Function Theorem ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Jacobi Method ◽  
Implicit Function ◽  
Third Order ◽  
Numerical Examples ◽  
The Real ◽  
The Third ◽  
Order Surface

AbstractBy Hamilton-Jacobi method, we study the problem of algebraic geodesics on the third-order surface. By the implicit function theorem, we proved the existences of the real geodesics which are the intersections of two algebraic surfaces, and we also give some numerical examples.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

The experience of employment of the mathematical cartography methods in cosmology

2017 ◽  
Vol 923 (5) ◽  
pp. 7-16
Author(s):  
A.V. Kavrayskiy
Keyword(s):  
Background Radiation ◽  
Three Dimensional ◽  
Spherical Coordinates ◽  
Linear Element ◽  
Microwave Background ◽  
Euclidian Space ◽  
Microwave Background Radiation ◽  
Rectangular Coordinates ◽  
The Universe ◽  
Length Distortion

The experience of mathematical modeling of the 3D-sphere in the 4D-space and projecting it by mathematical cartography methods in the 3D-Euclidian space is presented. The problem is solved by introduction of spherical coordinates for the 3D-sphere and their transformation into the rectangular coordinates, using the mathematical cartography methods. The mathematical relationship for calculating the length distortion mp(s) of the ds linear element when projecting the 3D-sphere from the 4-dimensional Euclidian space into three-dimensional Euclidian space is derived. Numerical examples, containing the modeling of the ds small linear element by spherical coordinates of 3D-sphere, projecting this sphere into the 3D-Euclidian space and length of ds calculating by means of its projection dL and size of distortion mp(s) are solved. Based on the model of the Universe known in cosmology as the 3D-sphere, the hypothesis of connection between distortion mp(s) and the known observed effects Redshift and Microwave Background Radiation is considered.

scholarly journals Modeling of dense well block point bar architecture based on geological vector information: A case study of the third member of Quantou Formation in Songliao Basin

2021 ◽  
Vol 13 (1) ◽  
pp. 39-48
Author(s):  
Chao Luo ◽  
Ailin Jia ◽  
Jianlin Guo ◽  
Wei Liu ◽  
Nanxin Yin ◽  
...  
Keyword(s):  
River Sediments ◽  
Three Dimensional ◽  
Songliao Basin ◽  
Point Bar ◽  
Meandering River ◽  
Architecture Model ◽  
The Third ◽  
Continuous Convergence ◽  
Vector Information ◽  
Architecture Modeling

Abstract Although stochastic modeling methods can achieve multiple implementations of sedimentary microfacies model in dense well blocks, it is difficult to realize continuous convergence of well spacing. Taking the small high-sinuosity meandering river sediments of the third member of Quantou Formation in Songliao Basin as an example, a deterministic modeling method based on geological vector information was explored in this article. Quantitative geological characteristics of point bar sediments were analyzed by field outcrops, modern sediments, and dense well block anatomy. The lateral extension distance, length, and spacing parameters of the point bar were used to quantitatively characterize the thickness, dip angle, and frequency of the lateral layer. In addition, the three-dimensional architecture modeling of the point bar was carried out in the study. The established three-dimensional architecture model of well X24-1 had continuous convergence near all wells, which conformed to the geological knowledge of small high-sinuosity meandering river, and verified the reliability of this method in the process of geological modeling in dense well blocks.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

Sign in / Sign up

Export Citation Format

Share Document