Faster access than browser!
62 relations: Angular momentum, Arnold Sommerfeld, Astronomy, Atomic nucleus, Bohr model, Bonnet's theorem, Carl Gustav Jacob Jacobi, Carter constant, Central force, Charles Coulson, Computer algebra system, Constant of motion, Cosmological constant, Coulomb's law, Dihydrogen cation, E. T. Whittaker, Einstein–Brillouin–Keller method, Electric field, Electron, Electrostatics, Elliptic coordinate system, Elliptic integral, Energy, Experimental mathematics, General relativity, George David Birkhoff, Gravitational field, Gravity, Henri Poincaré, Hooke's law, Hydrogen, Imaginary number, Implicit function, Inverse-square law, Ion, Jacobi integral, Jean Gaston Darboux, Joseph Liouville, Joseph-Louis Lagrange, Kepler problem, Kerr metric, Kinetic energy, Lagrangian point, Lambert W function, Laplace–Runge–Lenz vector, Leonhard Euler, Limiting case (mathematics), Liouville dynamical system, Momentum, Parametric equation, ..., Physics, Pierre-Simon Laplace, Planet, Potential energy, Prolate spheroidal coordinates, Runge–Kutta methods, Star, Three-body problem, Urbain Le Verrier, Weierstrass's elliptic functions, William Rowan Hamilton, Wolfgang Pauli. Expand index (12 more) »
Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.
New!!: Euler's three-body problem and Angular momentum · See more »
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored a large number of students for the new era of theoretical physics.
New!!: Euler's three-body problem and Arnold Sommerfeld · See more »
Astronomy
Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.
New!!: Euler's three-body problem and Astronomy · See more »
Atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment.
New!!: Euler's three-body problem and Atomic nucleus · See more »
Bohr model
In atomic physics, the Rutherford–Bohr model or Bohr model or Bohr diagram, introduced by Niels Bohr and Ernest Rutherford in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar to the structure of the Solar System, but with attraction provided by electrostatic forces rather than gravity.
New!!: Euler's three-body problem and Bohr model · See more »
Bonnet's theorem
In classical mechanics, Bonnet's theorem states that if n different force fields each produce the same geometric orbit (say, an ellipse of given dimensions) albeit with different speeds v1, v2,...,vn at a given point P, then the same orbit will be followed if the speed at point P equals v_.
New!!: Euler's three-body problem and Bonnet's theorem · See more »
Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.
New!!: Euler's three-body problem and Carl Gustav Jacob Jacobi · See more »
Carter constant
The Carter constant is a conserved quantity for motion around black holes in the general relativistic formulation of gravity.
New!!: Euler's three-body problem and Carter constant · See more »
Central force
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin: where \scriptstyle \vec is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and \scriptstyle \hat.
New!!: Euler's three-body problem and Central force · See more »
Charles Coulson
Charles Alfred Coulson (13 December 1910 – 7 January 1974) was a British applied mathematician, theoretical chemist and religious author.
New!!: Euler's three-body problem and Charles Coulson · See more »
Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
New!!: Euler's three-body problem and Computer algebra system · See more »
Constant of motion
In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion.
New!!: Euler's three-body problem and Constant of motion · See more »
Cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.
New!!: Euler's three-body problem and Cosmological constant · See more »
Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
New!!: Euler's three-body problem and Coulomb's law · See more »
Dihydrogen cation
The hydrogen molecular ion, dihydrogen cation, or, is the simplest molecular ion.
New!!: Euler's three-body problem and Dihydrogen cation · See more »
E. T. Whittaker
Edmund Taylor Whittaker FRS FRSE (24 October 1873 – 24 March 1956) was an English mathematician who contributed widely to applied mathematics, mathematical physics, and the theory of special functions.
New!!: Euler's three-body problem and E. T. Whittaker · See more »
Einstein–Brillouin–Keller method
The Einstein–Brillouin–Keller method (EBK) is a semiclassical method (named for Albert Einstein, Léon Brillouin, and Joseph B. Keller) used to compute eigenvalues in quantum-mechanical systems.
New!!: Euler's three-body problem and Einstein–Brillouin–Keller method · See more »
Electric field
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
New!!: Euler's three-body problem and Electric field · See more »
Electron
The electron is a subatomic particle, symbol or, whose electric charge is negative one elementary charge.
New!!: Euler's three-body problem and Electron · See more »
Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest.
New!!: Euler's three-body problem and Electrostatics · See more »
Elliptic coordinate system
In geometry, the elliptic(al) coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae.
New!!: Euler's three-body problem and Elliptic coordinate system · See more »
Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.
New!!: Euler's three-body problem and Elliptic integral · See more »
Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
New!!: Euler's three-body problem and Energy · See more »
Experimental mathematics
Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns.
New!!: Euler's three-body problem and Experimental mathematics · See more »
General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
New!!: Euler's three-body problem and General relativity · See more »
George David Birkhoff
George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem.
New!!: Euler's three-body problem and George David Birkhoff · See more »
Gravitational field
In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.
New!!: Euler's three-body problem and Gravitational field · See more »
Gravity
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.
New!!: Euler's three-body problem and Gravity · See more »
Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
New!!: Euler's three-body problem and Henri Poincaré · See more »
Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
New!!: Euler's three-body problem and Hooke's law · See more »
Hydrogen
Hydrogen is a chemical element with symbol H and atomic number 1.
New!!: Euler's three-body problem and Hydrogen · See more »
Imaginary number
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.
New!!: Euler's three-body problem and Imaginary number · See more »
Implicit function
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
New!!: Euler's three-body problem and Implicit function · See more »
Inverse-square law
The inverse-square law, in physics, is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity.
New!!: Euler's three-body problem and Inverse-square law · See more »
Ion
An ion is an atom or molecule that has a non-zero net electrical charge (its total number of electrons is not equal to its total number of protons).
New!!: Euler's three-body problem and Ion · See more »
Jacobi integral
In celestial mechanics, Jacobi's integral (also known as the Jacobi integral or Jacobi constant) is the only known conserved quantity for the circular restricted three-body problem.
New!!: Euler's three-body problem and Jacobi integral · See more »
Jean Gaston Darboux
Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician.
New!!: Euler's three-body problem and Jean Gaston Darboux · See more »
Joseph Liouville
Joseph Liouville FRS FRSE FAS (24 March 1809 – 8 September 1882) was a French mathematician.
New!!: Euler's three-body problem and Joseph Liouville · See more »
Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
New!!: Euler's three-body problem and Joseph-Louis Lagrange · See more »
Kepler problem
In classical mechanics, the Kepler problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them.
New!!: Euler's three-body problem and Kepler problem · See more »
Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon.
New!!: Euler's three-body problem and Kerr metric · See more »
Kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
New!!: Euler's three-body problem and Kinetic energy · See more »
Lagrangian point
In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies, wherein a small object, affected only by the gravitational forces from the two larger objects, will maintain its position relative to them.
New!!: Euler's three-body problem and Lagrangian point · See more »
Lambert W function
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(z).
New!!: Euler's three-body problem and Lambert W function · See more »
Laplace–Runge–Lenz vector
In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star.
New!!: Euler's three-body problem and Laplace–Runge–Lenz vector · See more »
Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
New!!: Euler's three-body problem and Leonhard Euler · See more »
Limiting case (mathematics)
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values.
New!!: Euler's three-body problem and Limiting case (mathematics) · See more »
Liouville dynamical system
In classical mechanics, a Liouville dynamical system is an exactly soluble dynamical system in which the kinetic energy T and potential energy V can be expressed in terms of the s generalized coordinates q as follows: T.
New!!: Euler's three-body problem and Liouville dynamical system · See more »
Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
New!!: Euler's three-body problem and Momentum · See more »
Parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
New!!: Euler's three-body problem and Parametric equation · See more »
Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
New!!: Euler's three-body problem and Physics · See more »
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.
New!!: Euler's three-body problem and Pierre-Simon Laplace · See more »
Planet
A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.
New!!: Euler's three-body problem and Planet · See more »
Potential energy
In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
New!!: Euler's three-body problem and Potential energy · See more »
Prolate spheroidal coordinates
Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located.
New!!: Euler's three-body problem and Prolate spheroidal coordinates · See more »
Runge–Kutta methods
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations.
New!!: Euler's three-body problem and Runge–Kutta methods · See more »
Star
A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity.
New!!: Euler's three-body problem and Star · See more »
Three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking an initial set of data that specifies the positions, masses, and velocities of three bodies for some particular point in time and then determining the motions of the three bodies, in accordance with Newton's laws of motion and of universal gravitation, which are the laws of classical mechanics.
New!!: Euler's three-body problem and Three-body problem · See more »
Urbain Le Verrier
Urbain Jean Joseph Le Verrier (11 March 1811 – 23 September 1877) was a French mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using only mathematics.
New!!: Euler's three-body problem and Urbain Le Verrier · See more »
Weierstrass's elliptic functions
In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass.
New!!: Euler's three-body problem and Weierstrass's elliptic functions · See more »
William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
New!!: Euler's three-body problem and William Rowan Hamilton · See more »
Wolfgang Pauli
Wolfgang Ernst Pauli (25 April 1900 – 15 December 1958) was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics.
New!!: Euler's three-body problem and Wolfgang Pauli · See more »
Redirects here:
CRTBP, Circular restricted three-body problem, Copenhagen Problem, Copenhagen problem, Darboux's problem, Euler three-body problem, Euler's three body problem, Euler-Jacobi problem, Problem of two centers, Problem of two centers of gravitation, Problem of two centres, Problem of two centres of gravitation, Problem of two fixed centers, Problem of two fixed centres, Pythagorean problem, Restricted 3 body problem, Restricted 3-body problem, Two-center Kepler problem, Two-centre Kepler problem, Velde's problem.
References
[1] https://en.wikipedia.org/wiki/Euler's_three-body_problem
