Elastic Collision - collision in which the total kinetic energy of a system of two colliding bodies is unchanged by the collision.
Inelastic Collision - collision in which the kinetic energy of the system is not conserved. Energy is always transferred from kinetic energy to other forms of energy, such as thermal energy or energy of sound.
The greatest loss of kinetic energy occurs on a collision when the two objects stick together, in which case the collision is called a completely inelastic collision.
In a closed, isolated system, the velocity of the center of mass of the system cannot be changed by a collision because, with the system isolated, there is no net external force to change it.
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Derivations not shown in book of equations 9-67 and 9-68 on p. 222 can be found in the .pdf file below.