18 Result(s)
within
English
Physics
Astronomy, Observations and Techniques
C. Marchal
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Chapter and Conference Paper
Qualitative Methods and Results in Celestial Mechanics
In a non integrable problem qualitative methods give partial but also rigorously demonstrated properties, they have been essentially developed by Poincaré, Sundman, Chazy, Khilmi, Merman, Sitnikov, Alexeev etc …
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Chapter and Conference Paper
Regularization of the Singularities of the N-Body Problem
The n-body problem has two types of singularities: the collisions of two or several bodies and “the infinite expansions in a bounded interval of time.”
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Chapter
Three-Body Problem Some Applications of the Tests of Escape
Some recent tests have given excellent results in the analysis of three-body systems with three equal masses. These analyses are here extended to systems of unequal masses and lead to the following.
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Chapter and Conference Paper
Round Table Discussion on Chaotic Motions
The importance of chaotic motions has been recognized only recently.
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Chapter
The Near-Resonance Theorem: Analysis of the Vicinity of Periodic Solutions of Analytic Differential Systems
The near-resonance theorem allows us to simplify the systems of differential equations and to study the vicinity and the stability of their periodic solutions. It leads to suitable transformations that cancel ...
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Chapter and Conference Paper
A Small Example of Arnold Diffusion
The Arnold diffusion occurs in the vicinity of most linearly stable solutions of non-integrable autonomous Hamiltonian systems with more than two degrees of freedom.
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Chapter and Conference Paper
Qualitative Analysis in the Few Body Problem
After a small illustrative example, the development of qualitative methods in Celestial Mechanics is presented in an essentially chronological way, from the early researches of particular solutions and new int...
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Chapter and Conference Paper
The Mystery of Pluto’s Mass
After a short presentation of the Pluto-Charon system and the history of its mass determinations some first reasons are presented that support the existence of a ring of billions of small satellites about Plut...
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Chapter
Chaos as the True Source of the Irreversibility of Time
After a first part about the various definitions of time, the main examples of irreversibilities are presented.
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Chapter
Analytic Hamiltonian Systems, the Vicinity of a Periodic Solution
After the presentation of ordinary analytic systems of differential equations, the successive simplifications allowing the study of a periodic solution and its vicinity are described.
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Chapter and Conference Paper
Astrodynamic Study of the Earth Rotation
Earth rotation and the position of poles are essential elements of climate. Since centuries the motion of the poles with respect to the Earth’s surface has remained very small, but this was not necessarily the...
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Chapter and Conference Paper
Henri Poincaré: A Decisive Contribution to Special Relativity
Maxwell’s electromagnetism equations and the old notions of Newtonian absolute time and Euclidian absolute space were contradictory with the impossibility of detection of the Earth’s absolute motion.
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Chapter
Tests of General Relativity Using Small Bodies of the Solar System
The tests of general relativity have two main purposes:
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To verify, or not, some consequences of the general relativity. The ST...
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Chapter and Conference Paper
The Family P 12 of the Three-Body Problem — the Simplest Family of Periodic Orbits, with Twelve Symmetries per Period
A beautiful plane eight-shaped orbit has been found by Alain Chenciner, Richard Montgomery and Caries Simo through the minimisation of the action between suitable limit conditions. The three masses are equal a...
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Chapter and Conference Paper
How the Method of Minimization of Action Avoids Singularities
The method of minimization of action is a powerful technique of proving the existence of particular and interesting solutions of the n-body problem, but it suffers from the possible interference of singularities....
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Chapter and Conference Paper
The General Solution of the Planar Laplace Problem
The famous Laplace problem is the three-body, secular, planetary problem. Its plane version has the great theoretical advantage of being integrable (Ferraz-Mello, private correspondence, 2001) and Ferraz-Mello...
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Chapter and Conference Paper
On the general solutions of Hilbert-Einstein field equations in vacuum
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Chapter and Conference Paper
General properties of three-body systems with Hill-type stability
