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Featherstone's Algorithm
Featherstone's algorithm is a technique used for computing the effects of forces applied to a structure of joints and links (an "open kinematic chain") such as a skeleton used in ragdoll physics. The Featherstone's algorithm uses a reduced coordinate representation. This is in contrast to the more popular Lagrange multiplier method, which uses maximal coordinates.Brian Mirtich's PhD Thesishas a very clear and detailed description of the algorithm. Baraff's papehas a discussion and comparison of both algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...s. References * External links Featherstone Multibody in Bullet Physics engine [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematic Chain
In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. Reuleaux, F., 187''The Kinematics of Machinery,''(trans. and annotated by A. B. W. Kennedy), reprinted by Dover, New York (1963) As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator.J. M. McCarthy and G. S. Soh, 2010''Geometric Design of Linkages,''Springer, New York. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called ''lower pairs'' and the surface contact joints critical to cams and gearing, called ''higher pairs.'' These joints are generally modele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skeleton
A skeleton is the structural frame that supports the body of most animals. There are several types of skeletons, including the exoskeleton, which is a rigid outer shell that holds up an organism's shape; the endoskeleton, a rigid internal frame to which the organs and soft tissues attach; and the hydroskeleton, a flexible internal structure supported by the hydrostatic pressure of body fluids. Vertebrates are animals with an endoskeleton centered around an axial vertebral column, and their skeletons are typically composed of bones and cartilages. Invertebrates are other animals that lack a vertebral column, and their skeletons vary, including hard-shelled exoskeleton (arthropods and most molluscs), plated internal shells (e.g. cuttlebones in some cephalopods) or rods (e.g. ossicles in echinoderms), hydrostatically supported body cavities (most), and spicules (sponges). Cartilage is a rigid connective tissue that is found in the skeletal systems of vertebrates and invert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ragdoll Physics
Ragdoll physics is a type of procedural animation used by physics engines, which is often used as a replacement for traditional static death animations in video games and Animation, animated films. As computers increased in power, it became possible to do limited real-time physical simulations, which made death animations more realistic. Early video games used manually created animations for a character’s death sequences. This had the advantage of low Central processing unit, CPU utilization, as the data needed to animate a "dying" character was chosen from a set number of pre-drawn frames. In contrast, a ragdoll is a collection of multiple rigid body, rigid bodies (each of which is ordinarily tied to a bone in the graphics engine's skeletal animation system) tied together by a system of constraints that restrict how the bones may move relative to each other. When the character dies, their body begins to collapse to the ground, honouring these restrictions on each of the joint ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Multiplier Method
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. Summary and rationale The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function or Lagrangian. In the general case, the Lagrangian is defined as \mathcal(x, \lambda) \equiv f(x) + \langle \lambda, g(x)\rangle for functions f, g; the notation \langle \cdot, \cdot \rangle denotes an inner product. The value \lambda is called the Lagrange multiplier. In simple case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...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. 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 physics is the subject that deals with these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
