The Experts below are selected from a list of 1563 Experts worldwide ranked by ideXlab platform
M M Aksirov - One of the best experts on this subject based on the ideXlab platform.
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a correction to the law of universal gravitation derived from the einstein hilbert equations
Russian Physics Journal, 2009Co-Authors: M M AksirovAbstract:A new form of the law of universal gravitation, more exact than that derived from the three Kepler Laws, is derived from the Einstein-Hilbert equations. Based on this result, a genesis of a secular displacement of the elliptic orbit perihelia is explained.
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A correction to the law of universal gravitation derived from the Einstein–Hilbert equations
Russian Physics Journal, 2009Co-Authors: M M AksirovAbstract:A new form of the law of universal gravitation, more exact than that derived from the three Kepler Laws, is derived from the Einstein-Hilbert equations. Based on this result, a genesis of a secular displacement of the elliptic orbit perihelia is explained.
Gert Heckman - One of the best experts on this subject based on the ideXlab platform.
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teaching the Kepler Laws for freshmen
The Mathematical Intelligencer, 2009Co-Authors: Maris Van Haandel, Gert HeckmanAbstract:One of the highlights of classical mechanics is the mathematical derivation of the three experimentally observed Kepler Laws of planetary motion from Newton’s Laws of motion and of gravitation. Newton published his theory of gravitation in 1687 in the Principia Mathematica [1]. After two short introductions, one with definitions and the other with axioms (the Laws of motion), Newton discussed the Kepler Laws in the first three sections of Book 1 (in just 40 pages, without ever mentioning the name of Kepler!) Kepler’s second law (motion is planar and equal areas are swept out in equal times) is an easy consequence of the conservation of angular momentum L = r × p, and holds in greater generality for any central force field. All this is explained well by Newton in Propositions 1 and 2. Kepler’s first law (planetary orbits are ellipses with the center of the force field at a focus) however is specific for the attractive 1/r force field. Using Euclidean geometry Newton derives in Proposition 11 that the Kepler Laws can only hold for an attractive 1/r force field. The reverse statement that an attractive 1/r force field leads to elliptical orbits Newton concludes in Corollary 1 of Proposition 13. Tacitly he assumes for this argument that the equation of motion F = ma has a unique solution for given initial position and initial velocity. Theorems about existence and uniqueness of solutions of such a differential equation have only been formulated and mathematically rigorously been proven in the 19th century. However there can be little doubt that Newton did grasp these properties of his equation F = ma [2]. Somewhat later in 1710 Jakob Hermann and Johan Bernoulli gave a direct proof of Kepler’s first law, which is still the standard proof for modern text books on classical mechanics [3]. One writes the position vector r in the plane of motion in polar coordinates r and θ. The trick is to transform the equation of motion ma = −kr/r with variable the time t into a second order differential
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teaching the Kepler Laws for freshmen
arXiv: Symplectic Geometry, 2007Co-Authors: Maris Van Haandel, Gert HeckmanAbstract:We present a natural proof of Kepler's law of ellipses in the spirit of Euclidean geometry. Moreover we discuss two existing Euclidean geometric proofs, one by Feynman in hist Lost Lecture from 1964 and the other by Newton in the Principia of 1687.
Bao Jiguang - One of the best experts on this subject based on the ideXlab platform.
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from nowton Laws to three Kepler Laws
College Mathematies, 2003Co-Authors: Bao JiguangAbstract:Three Kepler Laws, which describe planets' motion around the sun, are derived by using the law of universal gravitation and the second Newton law in mechanics.
Juri I. Neimark - One of the best experts on this subject based on the ideXlab platform.
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mathematical models in natural science and engineering
2003Co-Authors: Juri I. NeimarkAbstract:Dynamic system.- Fluid flowing-out from a vessel.- Equilibrium and auto-oscillations of fluid level in a vessel with simultaneous inflow and outflow.- Transitive process, equilibrium state and auto-oscillations.- Dynamics of water level in a reservoired hydropower station.- Energetic model of a heart.- Soiling a water reservoir with a bay and the Caspian Sea puzzles.- Exponential processes.- Populations coexistence dynamics.- Flow biological reactor.- Mathematical model of an immune response of a living organism to an infectious invastion.- Mathematic model for the community 'Manufacturers-Products-Managers'.- Linear oscillator.- Electromechanical analogies. Lagrange-Maxwell equations.- Galileo-Huygens watch.- Generator of electric oscillations.- Soft and hard regimes of exciting auto-oscillations.- Stochastic oscillator.- Instability and auto-oscillations caused by friction.- Forced oscillations of a linear oscillator.- Parametric excitation and stabilization.- Normal oscillations and beatings.- Stabilizing an inverted pendulum.- Controllable pendulum and a two-legged pacing.- Dynamic models for games, teaching and rational behaviour.- Perceptron and pattern recognition.- Kepler Laws and the two-body problem solved by Newton.- Distributed dynamic models in mechanics and physics.- Fundamental solution of the thermal conductivity equation.- Travelling waves and the dispersion equation.- Faraday-Maxwell theory of electromagnetism and Maxwell-Hertz electromagnetic waves.- Wave reflection and refraction.- Standing waves and oscillations of a bounded string.- Microparticle.- Space and time.- Speeding up relativistic microparticles in a cyclotron.- Mathematics as a language and as an operating system and models.- Geometrical, physical, analogous, mathematical and imitative types of modelling.- General scheme of methematical modelling.- Models of vibratory pile driving.- The fundamental mathematical model of the modern science and the theory of oscillations.- Mathematicalmodel as a fruitful idea of research. D-partition.- Idealization, mathematical correctness and reality.- Dynamical interpretation of the least square method and global searching optimization with an adaptive model.- Theoretic game model of the human society.
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Kepler Laws and the two-body problem solved by Newton
Foundations of Engineering Mechanics, 2003Co-Authors: Juri I. NeimarkAbstract:The two-body problem and its relations with some astronomic problems like black holes, universe extension and solar system evolution.
Gregory Gillian - One of the best experts on this subject based on the ideXlab platform.
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Sputnik, The Beep-Beep-Beep Heard Around the World: An Analysis of the Orbital Trajectory of Sputnik and its Reception in the Soviet Union
Open Works, 2019Co-Authors: Gregory GillianAbstract:The purpose of this undergraduate thesis in the fields of Mathematics and Russian Studies at the College of Wooster is to explore the mathematical and cultural significance of the launch of the first artificial Earth satellite, Sputnik 1, and how it was perceived by the Soviet Union and the rest of the world. The historical perception of this launch is established through discussion of the connected series of scientific achievements that led to the inevitable launch of the first artificial Earth satellite made by the Soviets as well as the analyzation of the initial press coverage after the launch. Focus is also given to the theory of orbits and Kepler Laws to establish a more technical understanding of the complications faced in order to launch a satellite into orbit
