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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] |
Deformable Bodies
In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding. Plastic deformation is observed in most materials, particularly metals, soils, rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can result. In brittle materials such as rock, concrete and bone, plasticity is caused pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Rotation Theorem
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. It also means that the composition of two rotations is also a rotation. Therefore the set of rotations has a group structure, known as a ''rotation group''. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically represented by a unit vector . Its product by the rotation angle is known as an axis-angle vector. The extension of the theorem to kinematics yields the concept of instant axis of rotation, a line of fixed points. In linear algebra terms, the theorem states that, in 3D space, any two Cartesian coordinate systems with a common origin are related by a rotation about some fixed axis. This also means that the product of two rot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general Basis (linear algebra), basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed ''elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be #Conventions by extrinsic rotations, extrinsic (rotations about the axes ''xyz'' of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it." Euler is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resultant Force
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. Calculating and visualizing the resultant force on a body is done through computational analysis, or (in the case of sufficiently simple systems) a free body diagram. The point of application of the resultant force determines its associated torque. The term ''resultant force'' should be understood to refer to both the forces and torques acting on a rigid body, which is why some use the term ''resultant force–torque''. Illustration The diagram illustrates simple graphical methods for finding the line of application of the resultant force of simple planar systems. #Lines of application of the actual forces and \scriptstyle \vec_ in the leftmost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical System
A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by Animal power, animals and Human power, people, by natural forces such as Wind power, wind and Water power, water, and by Chemical energy, chemical, Thermal energy, thermal, or electricity, electrical power, and include a system of mechanism (engineering), mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems. Renaissance natural philosophers identified six simple machines which were the elementary devices that put a load into motion, and calculated the ratio of output force to input fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-variant System
A time-variant system is a system whose output response depends on moment of observation as well as moment of input signal application. In other words, a time delay or time advance of input not only shifts the output signal in time but also changes other parameters and behavior. Time variant systems respond differently to the same input at different times. The opposite is true for time invariant systems (TIV). Overview There are many well developed techniques for dealing with the response of linear time invariant systems, such as Laplace and Fourier transforms. However, these techniques are not strictly valid for time-varying systems. A system undergoing slow time variation in comparison to its time constants can usually be considered to be time invariant: they are close to time invariant on a small scale. An example of this is the aging and wear of electronic components, which happens on a scale of years, and thus does not result in any behaviour qualitatively different from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on 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 1788 work, '' Mécanique analytique''. Lagrangian mechanics describes a mechanical system as a pair (M,L) consisting of a configuration space M and a smooth function L within that space called a ''Lagrangian''. By convention, L = T - V, where T and V are the kinetic and potential energy of the system, respectively. The stationary action principle requires that the action functional of the system derived from 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. Introduction Suppose there exists a bead sliding around on a wire, or a swinging simple p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. # When a body is acted upon by a force, the time rate of change of its momentum equals the force. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his '' Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. In the time since Newton, the conceptual content of classical physics has been reformulated in alternative ways, involving diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
