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Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits.  Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. .

Mathematics. --- Dynamics. --- Ergodic theory. --- Astrophysics. --- Physics. --- Dynamical Systems and Ergodic Theory. --- Statistical Physics and Dynamical Systems. --- Astrophysics and Astroparticles. --- History and Philosophical Foundations of Physics. --- Planetary Sciences. --- Three-body problem. --- Problem of three bodies --- Differentiable dynamical systems. --- Statistical physics. --- Planetary science. --- Mechanics, Analytic --- Planetary sciences --- Planetology --- Physics --- Mathematical statistics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Statistical methods --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Astronomical physics --- Astronomy --- Cosmic physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Force and energy --- Mechanics --- Statics --- Three-body problem

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Choose an application

• Reference Manager
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• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
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• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)