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Dynamical Simulation
Dynamical simulation, in computational physics, is the simulation of systems of objects that are free to move, usually in three dimensions according to Newton's laws of dynamics, or approximations thereof. Dynamical simulation is used in computer animation to assist animators to produce realistic motion, in industrial design (for example to simulate crashes as an early step in crash testing), and in video games. Body movement is calculated using time integration methods. Physics engines In computer science, a program called a physics engine is used to model the behaviors of objects in space. These engines allow simulation of the way bodies of many types are affected by a variety of physical stimuli. They are also used to create Dynamical simulations without having to know anything about physics. Physics engines are used throughout the video game and movie industry, but not all physics engines are alike. They are generally broken into real-time and the high precision, but these a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Physics
Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics - an area of study which supplements both theory and experiment. Overview In physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated. In such cases, numerical approximations are required. Computational phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Body Dynamics
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior. The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law (kinetics) or their derivative form, Lagrangian mechanics. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Equations (rigid Body Dynamics)
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. Their general vector form is : \mathbf \dot + \boldsymbol\omega \times \left( \mathbf \boldsymbol\omega \right) = \mathbf. where ''M'' is the applied torques and ''I'' is the inertia matrix. The vector \boldsymbol\alpha=\dot is the angular acceleration. In orthogonal principal axes of inertia coordinates the equations become : \begin I_1\,\dot_ + (I_3-I_2)\,\omega_2\,\omega_3 &= M_\\ I_2\,\dot_ + (I_1-I_3)\,\omega_3\,\omega_1 &= M_\\ I_3\,\dot_ + (I_2-I_1)\,\omega_1\,\omega_2 &= M_ \end where ''Mk'' are the components of the applied torques, ''Ik'' are the principal moments of inertia and ω''k'' are the components of the angular velocity. Derivation In an inertial frame of reference (subscripted "in"), Euler's second law s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collision Detection
Collision detection is the computational problem of detecting the intersection (Euclidean geometry), intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer graphics, computer games, computer simulations, robotics and computational physics. Collision detection algorithms can be divided into operating on 2D and 3D objects. Overview In physical simulation, experiments such as playing billiards, are conducted. The physics of bouncing billiard balls are well understood, under the umbrella of rigid body motion and elastic collisions. An initial description of the situation would be given, with a very precise physical description of the billiard table and balls, as well as initial positions of all the balls. Given a force applied to the cue ball (probably resulting from a player hitting the ball with their cue stick), we want to calculate the trajectories, precise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Volume
In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations by using simple volumes to contain more complex objects. Normally, simpler volumes have simpler ways to test for overlap. A bounding volume for a set of objects is also a bounding volume for the single object consisting of their union, and the other way around. Therefore, it is possible to confine the description to the case of a single object, which is assumed to be non-empty and bounded (finite). Uses Bounding volumes are most often used to accelerate certain kinds of tests. In ray tracing, bounding volumes are used in ray-intersection tests, and in many rendering algorithms, they are used for viewing frustum tests. If the ray or viewing frustum does not intersect the bounding volume, it cannot intersect the object contained wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Equations
200px, Leonhard Euler (1707–1783) In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them ''after'' Euler. Conjectures *Euler's conjecture (Waring's problem) *Euler's sum of powers conjecture * Euler's Graeco-Latin square conjecture Equations Usually, ''Euler's equation'' refers to one of (or a set of) differential equations (DEs). It is cus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equations
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics Engine
A physics engine is computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer graphics, video games and film ( CGI). Their main uses are in video games (typically as middleware), in which case the simulations are in real-time. The term is sometimes used more generally to describe any software system for simulating physical phenomena, such as high-performance scientific simulation. Description There are generally two classes of physics engines: real-time and high-precision. High-precision physics engines require more processing power to calculate very precise physics and are usually used by scientists and computer animated movies. Real-time physics engines—as used in video games and other forms of interactive computing—use simplified calculations and decreased accuracy to compute in time for the game to respon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Dynamics
''For classical dynamics at relativistic speeds, see relativistic mechanics#Relativistic dynamics, relativistic mechanics.'' Relativistic dynamics refers to a combination of Theory of relativity, relativistic and quantum concepts to describe the relationships between the motion and properties of a relativistic system and the forces acting on the system. What distinguishes relativistic dynamics from other physical theories is the use of an Scale invariance, invariant scalar evolution parameter to monitor the historical evolution of space-time events. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved. Twentieth century experiments showed that the physical description of microscopic and submicroscopic objects moving at or near the speed of light raised questions about such fundamental concepts as space, time, mass, and energy. The theoretical description of the physical phenomena required the integration of concept ... [...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] |
