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Quantum-Behaved Particle Swarm Optimization Algorithm Based on the two-body problem

Chinese Journal of Electronics 2019年第3期28卷 569-576页

作者： YAN Tao LIU Fengxian Institute of Big Data Science and Industry Shanxi University School of Computer and Information Technology Shanxi University Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education Guangzhou Institute of Electronic Technology Chinese Academy of Sciences University of Chinese Academy of Sciences

The present study proposes an improved Quantum-behaved particle swarm optimization algorithm based on the two-body problem model(QTPSO) for solving the problem that other quantum-behaved particle swarm optimization algorithms easily converge on local optimal solutions when solving complex nonlinear problems. In the proposed QTPSO algorithm, particles are categorised as core particles and edge particles. Once the position of the core particle is determined, the edge particle appears in the vicinity of the attractor exhibiting a high probability, and the attractor is obtained through the random weighted sum of the core particle and the optimal mean position. Through simulation of the motion of these two particles by applying the interaction of the particles in the two-body problem, this mechanism not only improves the diversity of the population, but also enhances the local search capacity. To validate the proposed algorithm, three groups of experimental results were obtained to compare the proposed algorithm with other swarm intelligence algorithms. The experimental results indicate the superiority of the QTPSO algorithm.

关键词： Quantum-behaved particle swarm optimization two-body problem Quantum potential well Wave function Nonlinear optimization problems

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GENERALIZED HOMOGENEOUS FUNCTIONS AND THE two-body problem

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Applied Mathematics and Mechanics(English Edition) 2005年第2期26卷 171-178页

作者： C.Biasi S.M.S.Godoy Departamento de Matemtica Instituto de Ciências Matemticas e de Computao Universidade de So Paulo-Campus de So Carlos Caixa Postal-668 13560-970 So Carlos-SP BrazilDepartamento de Matemtica Instituto de Ciências Matemticas e de Computao Universidade de So Paulo-Campus de So Carlos Caixa Postal-668 13560-970 So Carlos-SP Brazil

A generalization of the homogeneous function concept is *** application is done with a solution of the two-body problem.

关键词： homogeneous function generalized homogeneous function Kepler's second law two-body problem

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Re-examination of the two-body problem Using Our New General System Theory

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Journal of Philosophy Study 2021年第12期11卷 891-913页

作者： PAN Lingli CUI Weicheng Key Laboratory of Coastal Environment and Resources of Zhejiang Province(KLaCER) School of EngineeringWestlake UniversityHangzhouChina

It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic *** order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the *** two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system *** is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly *** considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body *** introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical *** is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity *** points out a new direction for the unification of different theories.

关键词： two-body problem new general system theory gravitational field psychic field classical mechanics quantum mechanics relativity theory

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Approximate and Exact GR-Solutions for the two-body problem

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Journal of High Energy Physics, Gravitation and Cosmology 2022年第3期8卷 690-723页

作者： Jan Helm Technical University of Berlin Berlin Germany

A binary gravitational rotator, also called the two-body problem, is a pair of masses m1, m2 moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) mr = m1m2/(m1+m2) orbiting around the total mass m = m1+m2 situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters gμν (m1, m2, R, a1, a2), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.

关键词： General Relativity two-body problem Gravitational Rotator Kerr Metric Generalized Kerr Metric

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The Criteria for Reducing Centrally Restricted Three-body problem to two-body problem

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International Journal of Astronomy and Astrophysics 2024年第1期14卷 1-19页

作者： Bijay Kumar Sharma Department of Electronics and Communication National Institute of Technology Patna India

Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius aH and planet mean radius RP and the ratio R1=RP/aH. Under very low R1 (less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R1=RP/aH =0.01 and 5.9862 × 10-3 respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.

关键词： Hill’s Radius two-body problem Fixed-Point Solution Lagrange Points Earth-Moon-Test Particle CRTBP

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