Perfectly Elastic Collision - Real World Examples

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A perfectly elastic collision is defined as a collision in which no kinetic energy is lost, meaning there is no sound or friction involved. This type of collision is primarily observed at the atomic level, such as in the interactions between gas particles. While perfectly elastic collisions are idealized concepts, they do not occur in the macroscopic world due to various energy losses. The discussion highlights the distinction between perfect and elastic collisions, emphasizing that perfect elasticity is a theoretical construct. Overall, perfectly elastic collisions are largely theoretical and not found in everyday experiences.
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What is a perfectly elastic collision?

Does it exist in the real world?
 
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Perfect elastic collision is a collision where no kinetic energy is lost during the collision (so there is no sound and no friction during the collision). This occurs on the atomic level (for example gas particles collide basically elastically)
 
i thought that's only an elastic collision?
 
I am going through this course on collision detection: https://siggraphcontact.github.io/ In this link is a PDF called course notes. Scrolling down to section 1.3, called constraints. In this section it is said that we can write bilateral constraints as ##\phi(\mathbf{x}) = 0## and unilateral constraints as ##\phi(\mathbf{x}) \ge 0##. I understand that, but then it says that these constraints call also be written as: $$\mathbf{J} \mathbf{u} = 0, \mathbf{J} \mathbf{u} \ge 0,$$ where...

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