Understanding the Coefficient of Restitution 4.3.2. Kinetic Definition of Restitution In the early 1800'sPoisson developeda kinetic definition of the coefficient of restitution.
The consequent results can then be used to provide the basis for anew definition for the energetic coefficient of restitution given for impacts inmultibody systems in the first place.
Coefficient of Restitution •Based on a kinematic definition, e is the absolute value of the ratio of the "velocity of separation"to the "velocity of approach": velocity of separation velocity of approach e = v 2 −v 1 u 2 −u 1 e = •Absolute value is taken to ensure that e is a positive number.
Following its inception by Newton (1686), and after undergoing several revisions regarding its definition, widely accepted solutions of impact problems remain to be incomplete without a proper definition of the restitution coefficient.
In contrast to Newton'skine-maticdefinition, Poisson'skinetic definition is based on the ratio of the magnitudes of the normal impulses corresponding to the periods of restitution and compression. In the absence of friction frictionless impact, the Poisson definition of the coefficient of normal ...
While Equation (4) is generally considered valid only for central collisions, the effective mass concept that is used within crush analysis and to derive Equations (2) and (3) renders Equation (4) a valid definition of the coefficient of restitution for non-central impacts, as well . 2 CALCULATING THE ...
FASCICLE XIV THE ANNALS OF "DUNAREA DE JOS" UNIVERSITY OF GALATI 58 According with definition of coefficient of restitution: () 1 1 1 1 2 v 1 1 1 v v u u k ⌋ ⌉ ⌊ ⌈ μ + εμ + μ μ + ε μ + =-= + = 2 1 1 el m m 1 E E k or μ + = 1 1 E E k 1 el 3.
For collinear collisions, this definition of the coefficient of restitution (velocity restitution) is the same as impulse restitution and energy restitution; see Brach (1991b).
If energy is lost in the collision then it follows that (u 1 - u 2) > - (v 1 - v 2) In order to solve numerical problems when energy is lost we use the COEFFICIENT OF RESTITUTION which is defined as) 4.(..... 2 1 2 1 u u v v e − − − = These equations must be remembered.
Introduction The coefficient of restitution ( COR) of two colliding objects is defined as the ratio of their relative speed after and before impact ... It is unclear whether this definition is sufficient or unnecessarily conservative.