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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 ...
However, once the solution is obtained, the final direction of motion is determined to contradict the assumed direction of the friction force, leading to a paradox. [ 1 ] This result is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with ...
Consider a block which can slide or stick on a table (see figure 1a). The motion of the block is described by the equation of motion, whereas the friction force is unknown (see figure 1b). In order to obtain the friction force, a separate force law must be specified which links the friction force to the associated velocity of the block.
At the macroscopic scale, it is applied for the investigation of the motion of contacting bodies (see Contact dynamics). For instance the bouncing of a rubber ball on a surface depends on the frictional interaction at the contact interface. Here the total force versus indentation and lateral displacement are of main concern.
Rigid body dynamics deals with the motion of objects that cannot change shape, size, or mass but can change orientation and position. To account for rotational energy and momentum, we must describe how force is applied to the object using a moment , and account for the mass distribution of the object using an inertia tensor .
The simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints.
The rigid body's motion is entirely determined by the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. Its inertia ellipsoid rolls, without slipping, on the invariable plane , with the center of the ellipsoid a constant height above the plane.
The force and torque vectors that arise in applying Newton's laws to a rigid body can be assembled into a screw called a wrench. A force has a point of application and a line of action, therefore it defines the Plücker coordinates of a line in space and has zero pitch. A torque, on the other hand, is a pure moment that is not bound to a line ...