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51-504: Babylon Project may refer to: The Babylon Project , a FreeSpace 2 Source Code Project A fictional space station construction program in the Babylon 5 television series Project Babylon , an Iraqi weapons program A fictional construction project involving the filling in of Tokyo Bay in the Patlabor series The Babylon Project,

102-432: A {\displaystyle F=ma} , is valid. Non-inertial reference frames accelerate in relation to another inertial frame. A body rotating with respect to an inertial frame is not an inertial frame. When viewed from an inertial frame, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it appears that there are other forces that enter

153-413: A Legendre transformation on the generalized coordinates, velocities and momenta; therefore, both contain the same information for describing the dynamics of a system. There are other formulations such as Hamilton–Jacobi theory , Routhian mechanics , and Appell's equation of motion . All equations of motion for particles and fields, in any formalism, can be derived from the widely applicable result called

204-514: A baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made of a large number of collectively acting point particles. The center of mass of a composite object behaves like a point particle. Classical mechanics assumes that matter and energy have definite, knowable attributes such as location in space and speed. Non-relativistic mechanics also assumes that forces act instantaneously (see also Action at

255-412: A configuration space M {\textstyle M} and a smooth function L {\textstyle L} within that space called a Lagrangian. For many systems, L = T − V , {\textstyle L=T-V,} where T {\textstyle T} and V {\displaystyle V} are the kinetic and potential energy of

306-533: A 2002 foundation established by Alexey Kuzmichev to preserve Iraqi antiquities Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Babylon Project . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Babylon_Project&oldid=1062333773 " Category : Disambiguation pages Hidden categories: Short description

357-997: A close relationship with geometry (notably, symplectic geometry and Poisson structures ) and serves as a link between classical and quantum mechanics . In this formalism, the dynamics of a system are governed by Hamilton's equations, which express the time derivatives of position and momentum variables in terms of partial derivatives of a function called the Hamiltonian: d q d t = ∂ H ∂ p , d p d t = − ∂ H ∂ q . {\displaystyle {\frac {\mathrm {d} {\boldsymbol {q}}}{\mathrm {d} t}}={\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {p}}}},\quad {\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}=-{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {q}}}}.} The Hamiltonian

408-663: A continuation of FreeSpace 2 , telling of a civil war between Earth and the GTVA. The FreeSpace Port , sometimes called FSPort, ports the original Descent: FreeSpace – The Great War to the FreeSpace 2 and SCP engine with many graphical enhancements, and serves as a base for many mods set in the FreeSpace: Great War era, such as Shrouding the Light and Awakenings . Silent Threat: Reborn similarly ports

459-416: A decrease in the magnitude of velocity " v " is referred to as deceleration , but generally any change in the velocity over time, including deceleration, is referred to as acceleration. While the position, velocity and acceleration of a particle can be described with respect to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in which

510-447: A distance ). The position of a point particle is defined in relation to a coordinate system centered on an arbitrary fixed reference point in space called the origin O . A simple coordinate system might describe the position of a particle P with a vector notated by an arrow labeled r that points from the origin O to point P . In general, the point particle does not need to be stationary relative to O . In cases where P

561-428: A fictitious centrifugal force and Coriolis force . A force in physics is any action that causes an object's velocity to change; that is, to accelerate. A force originates from within a field , such as an electro-static field (caused by static electrical charges), electro-magnetic field (caused by moving charges), or gravitational field (caused by mass), among others. Newton was the first to mathematically express

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612-729: A particular formalism based on Newton's laws of motion . Newtonian mechanics in this sense emphasizes force as a vector quantity. In contrast, analytical mechanics uses scalar properties of motion representing the system as a whole—usually its kinetic energy and potential energy . The equations of motion are derived from the scalar quantity by some underlying principle about the scalar's variation . Two dominant branches of analytical mechanics are Lagrangian mechanics , which uses generalized coordinates and corresponding generalized velocities in configuration space , and Hamiltonian mechanics , which uses coordinates and corresponding momenta in phase space . Both formulations are equivalent by

663-487: A reformulation of Lagrangian mechanics . Introduced by Sir William Rowan Hamilton , Hamiltonian mechanics replaces (generalized) velocities q ˙ i {\displaystyle {\dot {q}}^{i}} used in Lagrangian mechanics with (generalized) momenta . Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has

714-445: A single "umbrella" project (with the unified goal of enhancing the game) under the name FreeSpace 2 Source Code Project was formed. Initially led by Edward "Inquisitor" Gardner, the team is currently led by Tyler "DahBlount" Blount. Previous leaders also include Ian "Goober5000" Warfield, Taylor Richards, Cliff "Chief1983" Gordon and Fabian "The E" Woltermann. In addition, content update packs have been developed which take advantage of

765-411: A solid body into a collection of points.) In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The behavior of very small particles, such as the electron , is more accurately described by quantum mechanics .) Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom , e.g.,

816-464: Is a limiting case of the Poincaré group used in special relativity . The limiting case applies when the velocity u is very small compared to c , the speed of light . The transformations have the following consequences: For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally

867-408: Is based on the choice of mathematical formalism. Classical mechanics can be mathematically presented in multiple different ways. The physical content of these different formulations is the same, but they provide different insights and facilitate different types of calculations. While the term "Newtonian mechanics" is sometimes used as a synonym for non-relativistic classical physics, it can also refer to

918-401: Is called the equation of motion . As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity of the particle, for example: where λ is a positive constant, the negative sign states that the force is opposite the sense of the velocity. Then the equation of motion is This can be integrated to obtain where v 0

969-405: Is different from Wikidata All article disambiguation pages All disambiguation pages FreeSpace 2 Source Code Project Volition , the company responsible for developing the game FreeSpace 2 was bought by THQ in 2000. With Interplay Entertainment holding the licenses for the FreeSpace series, Volition could not continue to develop the series. Without any viable use for

1020-412: Is equal to the change in kinetic energy E k of the particle: Conservative forces can be expressed as the gradient of a scalar function, known as the potential energy and denoted E p : If all the forces acting on a particle are conservative, and E p is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing

1071-426: Is moving relative to O , r is defined as a function of t , time . In pre-Einstein relativity (known as Galilean relativity ), time is considered an absolute, i.e., the time interval that is observed to elapse between any given pair of events is the same for all observers. In addition to relying on absolute time , classical mechanics assumes Euclidean geometry for the structure of space. The velocity , or

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1122-422: Is non-conservative. The kinetic energy E k of a particle of mass m travelling at speed v is given by For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. The work–energy theorem states that for a particle of constant mass m , the total work W done on the particle as it moves from position r 1 to r 2

1173-416: Is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the conservation of energy ), and the particle is slowing down. This expression can be further integrated to obtain the position r of

1224-515: Is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is a = d v /d t , the second law can be written in the simplified and more familiar form: So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation , which

1275-530: The Silent Threat expansion for Descent: FreeSpace into the FreeSpace 2 SCP engine. Classical mechanics This is an accepted version of this page Classical mechanics is a physical theory describing the motion of objects such as projectiles , parts of machinery , spacecraft , planets , stars , and galaxies . The development of classical mechanics involved substantial change in

1326-511: The forces applied to it. Classical mechanics also describes the more complex motions of extended non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass". (These generalizations/extensions are derived from Newton's laws, say, by decomposing

1377-429: The forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics . Dynamics goes beyond merely describing objects' behavior and also considers the forces which explain it. Some authors (for example, Taylor (2005) and Greenwood (1997) ) include special relativity within classical dynamics. Another division

1428-451: The principle of least action . One result is Noether's theorem , a statement which connects conservation laws to their associated symmetries . Alternatively, a division can be made by region of application: For simplicity, classical mechanics often models real-world objects as point particles , that is, objects with negligible size. The motion of a point particle is determined by a small number of parameters : its position, mass , and

1479-413: The rate of change of displacement with time, is defined as the derivative of the position with respect to time: In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at 60 − 50 = 10 km/h . However, from

1530-463: The speed of light . With objects about the size of an atom's diameter, it becomes necessary to use quantum mechanics . To describe velocities approaching the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. Some modern sources include relativistic mechanics in classical physics, as representing the field in its most developed and accurate form. Classical mechanics

1581-565: The stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his presentation to the Turin Academy of Science in 1760 culminating in his 1788 grand opus, Mécanique analytique . Lagrangian mechanics describes a mechanical system as a pair ( M , L ) {\textstyle (M,L)} consisting of

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1632-539: The 18th and 19th centuries, extended beyond earlier works; they are, with some modification, used in all areas of modern physics. If the present state of an object that obeys the laws of classical mechanics is known, it is possible to determine how it will move in the future , and how it has moved in the past. Chaos theory shows that the long term predictions of classical mechanics are not reliable. Classical mechanics provides accurate results when studying objects that are not extremely massive and have speeds not approaching

1683-402: The equations of motion solely as a result of the relative acceleration. These forces are referred to as fictitious forces , inertia forces, or pseudo-forces. Consider two reference frames S and S' . For observers in each of the reference frames an event has space-time coordinates of ( x , y , z , t ) in frame S and ( x' , y' , z' , t' ) in frame S' . Assuming time is measured

1734-407: The line connecting A and B , while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces. If a constant force F is applied to a particle that makes a displacement Δ r , the work done by the force is defined as the scalar product of the force and displacement vectors: More generally, if the force varies as a function of position as

1785-449: The mathematical methods invented by Newton, Gottfried Wilhelm Leibniz , Leonhard Euler and others to describe the motion of bodies under the influence of forces . Later, methods based on energy were developed by Euler, Joseph-Louis Lagrange , William Rowan Hamilton and others, leading to the development of analytical mechanics (which includes Lagrangian mechanics and Hamiltonian mechanics ). These advances, made predominantly in

1836-405: The mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames . An inertial frame is an idealized frame of reference within which an object with zero net force acting upon it moves with a constant velocity; that is, it is either at rest or moving uniformly in a straight line. In an inertial frame Newton's law of motion, F = m

1887-453: The methods and philosophy of physics. The qualifier classical distinguishes this type of mechanics from physics developed after the revolutions in physics of the early 20th century , all of which revealed limitations in classical mechanics. The earliest formulation of classical mechanics is often referred to as Newtonian mechanics . It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton , and

1938-526: The particle as a function of time. Important forces include the gravitational force and the Lorentz force for electromagnetism . In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B , it follows that B must exert an equal and opposite reaction force , − F , on A . The strong form of Newton's third law requires that F and − F act along

1989-409: The particle moves from r 1 to r 2 along a path C , the work done on the particle is given by the line integral If the work done in moving the particle from r 1 to r 2 is the same no matter what path is taken, the force is said to be conservative . Gravity is a conservative force, as is the force due to an idealized spring , as given by Hooke's law . The force due to friction

2040-406: The perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as −10 km/h where the sign implies opposite direction. Velocities are directly additive as vector quantities ; they must be dealt with using vector analysis . Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector u = u d and the velocity of

2091-401: The potential energies corresponding to each force The decrease in the potential energy is equal to the increase in the kinetic energy This result is known as conservation of energy and states that the total energy , is constant in time. It is often useful, because many commonly encountered forces are conservative. Lagrangian mechanics is a formulation of classical mechanics founded on

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2142-467: The presumed-defunct Beyond the Red Line each tell a side story based on the humans and robotic Cylons of the 2004 Battlestar Galactica television series. Another science fiction television series based project is The Babylon Project , based on the critically acclaimed Babylon 5 . All three of these projects are implementing their own Newtonian flight physics . The demo of The Babylon Project

2193-406: The relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law": The quantity m v is called the ( canonical ) momentum . The net force on a particle

2244-440: The same direction, this equation can be simplified to: Or, by ignoring direction, the difference can be given in terms of speed only: The acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time): Acceleration represents the velocity's change over time. Velocity can change in magnitude, direction, or both. Occasionally,

2295-471: The same in all reference frames, if we require x = x' when t = 0 , then the relation between the space-time coordinates of the same event observed from the reference frames S' and S , which are moving at a relative velocity u in the x direction, is: This set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform ). This group

2346-400: The second object by the vector v = v e , where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is: Similarly, the first object sees the velocity of the second object as: When both objects are moving in

2397-419: The source code, Volition's Dave Baranec released the source code for FreeSpace 2 ' s game engine on 25 April 2002. This allowed modders the possibility of modifying the game engine almost without limitations. However, because the source code is under a noncommercial license, it does not qualify as free and open source software . To prevent a plethora of different versions of the game from appearing,

2448-436: The system, respectively. The stationary action principle requires that the action functional of the system derived from L {\textstyle L} must remain at a stationary point (a maximum , minimum , or saddle ) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Hamiltonian mechanics emerged in 1833 as

2499-498: The upgraded game engine. These packs include higher-poly models and higher resolution textures. The end result of this project is to create a graphically superior (and far more flexible) game engine, while still retaining all of the gameplay elements that made FreeSpace 2 successful. The primary project FS2 Open takes advantage of the upgraded engine for FreeSpace 2 . Most of the other projects are based on science-fiction television shows or movies. Diaspora: Shattered Armistice and

2550-759: Was downloaded 100,000 times within two weeks of its announcement, and was reported on Apple.com and in France's Joystick game magazine. There are several projects to recreate established video games using the FS2 Open engine. These include Star Fox: Event Horizon for the Star Fox universe, and Wing Commander Saga for the Wing Commander universe. Some notable original mods and campaigns have been created, such as Wings of Dawn which takes place in an anime-style world, and Blue Planet which offers

2601-413: Was traditionally divided into three main branches. Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment. Kinematics describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering

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