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Sitnikov Problem
The Sitnikov problem is a restricted version of the three-body problem named after Russian mathematician Kirill Alexandrovitch Sitnikov that attempts to describe the movement of three celestial bodies due to their mutual gravitational attraction. A special case of the Sitnikov problem was first discovered by the American scientist William Duncan MacMillan in 1911, but the problem as it currently stands wasn't discovered until 1961 by Sitnikov. Definition The system consists of two primary bodies with the same mass \left(m_1 = m_2 = \tfrac\right), which move in circular or elliptical Kepler orbits around their center of mass. The third body, which is substantially smaller than the primary bodies and whose mass can be set to zero (m_3 = 0), moves under the influence of the primary bodies in a plane that is perpendicular to the orbital plane of the primary bodies (see Figure 1). The origin of the system is at the focus of the primary bodies. A combined mass of the primary bodies m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sitnikov Problem Konfiguration
Sitnikov is a surname. Notable people with the surname include: * Vasily Sitnikov (1915–1987), Russian painter * Alexei Sitnikov Alexei Alexandrovich Sitnikov (russian: Алексей Александрович Ситников; born 23 May 1986) is a former competitive ice dancer. Competing for Azerbaijan with Julia Zlobina, he is the 2013 Golden Spin of Zagreb champion, ... (born 1986), Russian figure skater {{Short pages monitor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-body Problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. The three-body problem is a special case of the n-body problem, -body problem. Unlike two-body problems, no general closed-form solution exists, as the resulting dynamical system is chaos theory, chaotic for most initial conditions, and numerical methods are generally required. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, Earth, and the Sun. In an extended modern sense, a three-body problem is any problem in classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirill Alexandrovitch Sitnikov
Kirill is a male given name, deriving from the Greek name Κύριλλος (Kyrillos) which in turn derives from Greek κύριος (kyrios) "lord". There are many variant forms of the name: Cyril, Cyrill, Kyrill, Kiryl, Kirillos, Kyryl, Kiril, Kyrylo, Kiro. Kirill may refer to: People *Kirill I of Moscow (born 1946), Russian Patriarch of Moscow and all Russia *Kirill Vladimirovich, Grand Duke of Russia *Kirill Alekseenko (born 1997), Russian chess grandmaster *Kirill Aleshin (born 1997), Russian ice dancer *Kirill Alexeyev (born 1981), Russian ice hockey player *Kirill Bichutsky (born 1984), American photographer, businessman *Kirill Dmitriev (born 1975), Russian businessman *Kirill Eskov (born 1956), Russian writer *Kirill Florensky (1915–1982), Russian geochemist and planetologist *Kirill Formanchuk, Russian activist for motorists' rights *Kirill Gerasimov (born 1971), Russian poker player *Kirill Gerstein (born 1979), Russian pianist *Kirill Gevorgian (born 1953), Russian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Duncan MacMillan
William Duncan MacMillan (July 24, 1871 – November 14, 1948) was an American mathematician and astronomer on the faculty of the University of Chicago. He published research on the applications of classical mechanics to astronomy, and is noted for pioneering speculations on physical cosmology. For the latter, Helge Kragh noted, "the cosmological model proposed by MacMillan was designed to lend support to a cosmic optimism, which he felt was threatened by the world view of modern physics." Biography He was born in La Crosse, Wisconsin, to D. D. MacMillan, who was in the lumber business, and Mary Jane McCrea. His brother, John H. MacMillan, headed the Cargill Corporation from 1909 to 1936. MacMillan graduated from La Crosse High School in 1888. In 1889, he attended Lake Forest College, then entered the University of Virginia. Later in 1898, he earned an A.B. degree from Fort Worth University, which was then a Methodist university in Texas. He performed his graduate work at the Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately The modern notation of Newton's law involving was introduced in the 1890s by C. V. Boys. The first impl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3 More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.''Analytical Mechanics'', L.N. Hand, J.D. Finch, Cambridge University Press, 2008, The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Calculus
In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point. Differential calculus and integral calculus are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrable System
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, such that its behaviour has far fewer degrees of freedom than the dimensionality of its phase space; that is, its evolution is restricted to a submanifold within its phase space. Three features are often referred to as characterizing integrable systems: * the existence of a ''maximal'' set of conserved quantities (the usual defining property of complete integrability) * the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability) * the explicit determination of solutions in an explicit functional form (not an intrinsic property, but something often referred to as solvability) Integrable systems may be seen as very different in qualitative character from mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
