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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 rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...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 (or desired) 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 in the familiar use of the word chain, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skeleton
A skeleton is the structural frame that supports the body of an animal. There are several types of skeletons, including the exoskeleton, which is the stable outer shell of an organism, the endoskeleton, which forms the support structure inside the body, and the hydroskeleton, a flexible internal skeleton supported by fluid pressure. Vertebrates are animals with a vertebral column, and their skeletons are typically composed of bone and cartilage. Invertebrates are animals that lack a vertebral column. The skeletons of invertebrates vary, including hard exoskeleton shells, plated endoskeletons, or Sponge spicule, spicules. Cartilage is a rigid connective tissue that is found in the skeletal systems of vertebrates and invertebrates. Etymology The term ''skeleton'' comes . ''Sceleton'' is an archaic form of the word. Classification Skeletons can be defined by several attributes. Solid skeletons consist of hard substances, such as bone, cartilage, or cuticle. These can be further ... [...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 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 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 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 joints' motion, which often looks more realistic. Th ... [...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 equality 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. 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. The method can be summarized as follows: in order to find the maximum or minimum of a function f(x) subjected to the equality constraint g(x) = 0, form the Lagrangian function :\mathcal(x, \lambda) = f(x) + \lambda g(x) and find the stationary points of \mathcal considered as a function of x and the Lagrange mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of 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 perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects result in displacements, or 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, Kepler, Huygens, and 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 ... [...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] |
