Game Development Reference
In-Depth Information
the objects to deform. (See the sidebar “Kinetic Energy” on page 106 for further details on
this topic.) When the deformation in the objects is permanent, energy is lost and thus
kinetic energy is not conserved.
Kinetic Energy
Kinetic energy is a form of energy associated with moving bodies. It is equal to the energy
required to accelerate the body from rest, which is also equal to the energy required to
bring the moving body to a stop. As you might expect, kinetic energy is a function of
the body's speed, or velocity, in addition to its mass. The formula for linear kinetic energy
is:
KE linear = (1/2) m v 2
Angular, or rotational, kinetic energy is a function of the body's inertia and angular
velocity:
KE angular = (1/2) I ω 2
Conservation of kinetic energy between two colliding bodies means that the sum of
kinetic energy of both bodies prior to impact is equal to the sum of the kinetic energy
of both bodies after impact:
m 1 v 2 1- + m 2 v 2 2- = m 1 v 2 1+ + m 2 v 2 2+
Collisions that involve losses in kinetic energy are said to be inelastic , or plastic , colli‐
sions. For example, if you throw two clay balls against each other, their kinetic energy
is converted to permanent strain energy in deforming the clay balls, and their collision
response—that is, their motion after impact—is less than spectacular. If the collision is
perfectly inelastic , then the two balls of clay will stick to each other and move together
at the same velocity after impact. Collisions where kinetic energy is conserved are called
perfectly elastic . In these collisions, the sum of kinetic energy of all objects before the
impact is equal to the sum of kinetic energy of all objects after the impact. A good
example of elastic impact (though not perfectly elastic) is the collision between two
billiard balls where the ball deformation is negligible and certainly not permanent under
normal circumstances.
Of course, in reality, impacts are somewhere between perfectly elastic and perfectly
inelastic. This means that for rigid bodies, which don't change shape at all, we'll have to
rely on an empirical relation to quantify the degree of elasticity of the impact(s) that
we're trying to simulate. The relation that we'll use is the ratio of the relative separation
velocity to the relative approach velocity of the colliding objects:
 
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