Richard Paul McGehee (born 20 September 1943 in San Diego) [1] is an American mathematician, who works on dynamical systems with special emphasis on celestial mechanics. [2]
McGehee received from Caltech in 1964 his bachelor's degree and from University of Wisconsin–Madison in 1965 his master's degree and in 1969 his Ph.D. under Charles C. Conley with thesis Homoclinic orbits in the restricted three body problem. [3] As a postdoc he was at the Courant Institute of Mathematical Sciences of New York University. In 1970 he became an assistant professor and in 1979 a full professor at the University of Minnesota in Minneapolis, where he was from 1994 to 1998 the director of the Center for the Computation and Visualization of Geometric Structures. [4] He has been at the University of Minnesota since 1970.
In the 1970s he introduced a coordinate transformation (now known as the McGehee transformation) which he used to regularize singularities arising in the Newtonian three-body problem. In 1975 he, with John N. Mather, proved that for the Newtonian collinear four-body problem there exist solutions which become unbounded in a finite time interval. [5] [6] [7]
In 1978 he was an Invited Speaker on the subject of Singularities in classical celestial mechanics at the International Congress of Mathematicians in Helsinki.
In physics, gravity (from Latin gravitas 'weight') is a fundamental interaction primarily observed as mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. Due to his scientific success, influence and his discoveries, he has been deemed "the philosopher par excellence of modern science."
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In regular perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics to astronomical objects, such as stars and planets, to produce ephemeris data.
The year 1975 in science and technology involved some significant events, listed below.
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state. In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies is governed by the principles of classical mechanics. In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by Newton's laws of motion. These principles can be equivalently expressed more abstractly by Hamiltonian mechanics or Lagrangian mechanics.
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
John Norman Mather was a mathematician at Princeton University known for his work on singularity theory and Hamiltonian dynamics. He was descended from Atherton Mather (1663–1734), a cousin of Cotton Mather. His early work dealt with the stability of smooth mappings between smooth manifolds of dimensions n and p. He determined the precise dimensions (n,p) for which smooth mappings are stable with respect to smooth equivalence by diffeomorphisms of the source and target.
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem. The n-body problem in general relativity is considerably more difficult to solve due to additional factors like time and space distortions.
Terence Gaffney is an American mathematician who has made fundamental contributions to singularity theory – in particular, to the fields of singularities of maps and equisingularity theory.
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Anton V. Zorich is a Russian mathematician at the Institut de mathématiques de Jussieu. He is the son of Vladimir A. Zorich. He received his Ph.D. from Moscow State University under the supervision of Sergei Novikov.
Alain Chenciner is a French mathematician, specializing in dynamical systems with applications to celestial mechanics.
Peter John Olver is a British-American mathematician working in differential geometry.
Mathematical Methods of Classical Mechanics is a textbook by mathematician Vladimir I. Arnold. It was originally written in Russian, and later translated into English by A. Weinstein and K. Vogtmann. It is aimed at graduate students.
In mathematics, the Simon problems are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential.
Zhihong "Jeff" Xia is a Chinese-American mathematician.
Antonio Giorgilli is an Italian mathematical physicist, known for his work on the perturbative theory of Hamiltonian systems with applications to studies of orbital stability for major and minor planets.
In celestial mechanics, a central configuration is a system of point masses with the property that each mass is pulled by the combined gravitational force of the system directly towards the center of mass, with acceleration proportional to its distance from the center. Central configurations are studied in n-body problems formulated in Euclidean spaces of any dimension, although only dimensions one, two, and three are directly relevant for celestial mechanics in physical space.
Luigi Chierchia is an Italian mathematician, specializing in nonlinear differential equations, mathematical physics, and dynamical systems.