As a scientific discipline, applied mechanics derives many of its principles and methods from the Physical sciences (in particular, Mechanics and Classical Mechanics), from Mathematics and, increasingly, from Computer Science. As such, Applied Mechanics shares similar methods, theories, and topics with Applied Physics, Applied Mathematics, and Computational Science.

As an enabling discipline, applied mechanics has received impetus from the study of natural phenomena such as orbits of planets, circulation of blood, locomotion of animals, crawling of cells, formation of mountains, and propagation of seismic waves. Such studies have resulted in disciplines such as celestial mechanics, biomechanics and geomechanics.

As a practical discipline, applied mechanics has also advanced by participating in major inventions throughout history, such as buildings, ships, automobiles, railways, petroleum refineries, engines, airplanes, nuclear reactors, composite materials, computers, and medical implants. In such connections, the discipline is also known as ”Engineering Mechanics”, often practiced within Civil Engineering, Mechanical Engineering, Construction Engineering, Materials Science and Engineering, Aerospace Engineering, Chemical Engineering, Electrical Engineering, Nuclear Engineering, Structural engineering and Bioengineering.

Adapted from the Wikipedia article Applied mechanics, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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circular orbit is the orbit of any point of an object rotating around a fixed axis.

Below we consider a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the plane of motion.

In this case not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version.

Adapted from the Wikipedia article Circular orbit, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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Sokolov did research on the ”n”-body problem for nearly 50 years. He summarized his work in the 1951 book ”Singular trajectories of a system of free material points” (Russian). He did research on functional equations and on such practical problems as the filtration of groundwater. He also did research on celestial mechanics and hydromechanics.

Sokolov is also known for ‘the averaging method with functional corrections’ or ‘the Sokolov method’. This method is for finding approximate solutions to differential and integral equations.

Sokolov wrote the book ”The method of averaging of functional corrections” (1967), in which he summaries his many important work. He wrote the book at an elementary level. First part of the book discusses applications of his method to problems which can be modelled by linear integral equations with constant limits. A number of different sufficient conditions for the approximations to converge and presents error estimates were given. The next three parts of the book first examines the problems which can be modelled by nonlinear integral equations with constant limits and then extend the analysis to the situation where the upper limit is variable. In the final part of the book, Sokolov’s methods to integral equations of mixed type are examined. He also presented some generalizations of the method in a number of appendices.

Adapted from the Wikipedia article Yurii Dmitrievich Sokolov, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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In (1910) he published “Discrete elements of matter and radiation”, “Corrientes marinas” (1941) and, to gain entry to the Royal Academy of the Spanish Language, the volume “Neologismos, arcanismos in plàtica de ingenieros” (1946). As an encyclopedist, he authored several articles in the Espasa Encyclopedia, including those on Celestial Mechanics, the Moon and relativity.

Adapted from the Wikipedia article Esteban Terradas i Illa, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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symplectic integrator (SI) is a numerical integration scheme for a specific group of differential equations related to classical mechanics and symplectic geometry. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in molecular dynamics, discrete element methods, accelerator physics, and celestial mechanics.

Adapted from the Wikipedia article Symplectic integrator, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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The true longitude l, can be calculated as follows:

l=bar{omega} + nu,

where:

*bar{omega}, is longitude of orbit’s periapsis,

*nu, is orbit’s true anomaly.

Category:Astrodynamics

Category:Celestial mechanics

el:Αληθινό γεωγραφικό μήκος

zh:真黃經
Adapted from the Wikipedia article True longitude, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton’s laws of motion and Newton’s law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton’s laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun).

Adapted from the Wikipedia article Orbital mechanics, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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For an object falling from infinity in a capture orbit, the time it takes from a given position to fall to the central point mass is the same as the free-fall time, except for a constant frac{4}{3pi} ≈ 0.42.

Category:Celestial mechanics
Adapted from the Wikipedia article Free-fall time, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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In 1947, there began an intense period of cooperative research on celestial mechanics between Clemence’s office, Eckert’s group at Columbia and Yale University Observatory, under the direction of Dirk Brouwer, a former collaborator of Eckert’s on punched cards.

Adapted from the Wikipedia article Gerald Maurice Clemence, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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Professor Archie Edminston Roy (born 1924 June 24), was educated at Hillhead High School and the University of Glasgow. He is married to Frances with three sons; Dr. Archie W N Roy, Ian Roy and David Roy.

Professor Roy is a Fellow of the Royal Society of Edinburgh, the Royal Astronomical Society, and the British Interplanetary Society. He is also a Member and past president of the Society for Psychical Research and Founding President of The Scottish Society for Psychical Research.

The asteroid [http://scully.harvard.edu/~cgi/MPEph.COM?su=t&Obj=05806 (5806) Archieroy] is named after him, with a registration in the IAU’s Minor planet center.

He has also been elected a member of the European Academy of Arts, Sciences and the Humanities. He is a Patron of the Churches Fellowship (Scotland) for Psychical and Spiritual Studies and a member of the Scientific and Medical Network.

Archie Roy conducts research in astrodynamics, celestial mechanics, archaeoastronomy, psychical research, and neural networks.

In addition Roy has published 20 books, six of them novels, some 70 scientific papers and scores of articles. His books have been published in the United Kingdom, United States, France, Russia, Italy and India.

In 2004 he was awarded the Myers Memorial Medal for outstanding contributions to psychical research by the Society for Psychical Research.

Adapted from the Wikipedia article Archie Roy, under the G. N. U. Free Documentation License. Please also see http://en.wikipedia.org/wiki

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